Probability — Class 10 Maths PYQs

In a family of two children, the probability of having at least one girl is :

If a letter of English alphabet is chosen at random, then the probability of this letter to be a consonant is:

The probability that a leap year selected at random will contain $53$ Sundays and $53$ Mondays, is :

In a group of 20 people, 5 can't swim. If one person is selected at random, then the probability that he/she can swim, is

In a survey, it is found that every fifth person has a vehicle. The probability of a person NOT having a vehicle is,

In a lottery, there are $5$ prizes and $20$ blanks. The probability of getting a prize is:

Assertion (A) : The probability that a leap year has $53$ Mondays is $\frac{2}{7}$.
Reason (R) : The probability that a non-leap year has $53$ Mondays is $\frac{5}{7}$.

A bag contains 5 pink, 8 blue and 7 yellow balls. One ball is drawn at random from the bag. What is the probability of getting neither a blue nor a pink ball?

The probability for a leap year (selected at random) to have $52$ Mondays and $53$ Sundays is :

The probability that in a family of three children, there will be at least two boys, is :

A bag contains $3$ red balls, $5$ white balls and $7$ black balls. The probability that a ball drawn from the bag at random will be neither red nor black is :

From the letters of the word "MOBILE", a letter is selected at random. The probability that the selected letter is a vowel, is :

Two friends were born in the year $2000$. The probability that they have the same birthday is :

In a cricket match, a batsman hits the boundary $7$ times out of the $42$ balls he plays. The probability of his not hitting a boundary is :

If in a lottery, there are $10$ prizes and $30$ blanks, then the probability of winning a prize is :

Letters A to F are mentioned on six faces of a die such that each face has a different letter. Two such die are thrown simultaneously. The probability that vowels turn up on both the dice is :

A bag contains red balls and black balls in the ratio $3:7$. A ball is drawn at random. The probability that ball so drawn is black in colour, is

A piggy bank contains ₹ 1 coins and ₹ 2 coins in the ratio 9 : 11 respectively. The piggy bank is accidently dropped and a coin pops out of it. The probability that it is a ₹ 2 coin is

A bag contains red coloured, blue coloured and green coloured balls in the ratio $2 : 3 : 4$. A ball is drawn at random from the given bag. The probability that the ball so drawn being not of blue colour is

A die is thrown once. Probability of getting a number other than $3$ is :

A letter is selected from the letters of the word FEBRUARY. The
probability that it is a vowel is:

Assertion (A): From a bag containing 5 red balls, 2 white balls and
3 green balls, the probability of drawing a non-white ball
is $\frac{4}{5}$
Reason (R) : For any event E, $P(E) + P (not E) = 1$

Assertion (A): The probability of a certain event E is 1.
Reason (R): The sum of probabilities of all elementary events of an experiment is 1.

From a bag containing yellow, red and green balls, the probability of drawing a yellow or red ball is equal to that of drawing a green ball. The probability of drawing a green ball from the bag is :

Assertion (A): The events "getting $2$" and "not getting $2$" in a single throw of an unbiased die are not equally likely events.
Reason (R): The probability of getting $2$ in a single throw of an unbiased die is $\frac{1}{6}$.
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(C) Assertion (A) is true, but Reason (R) is false.
(D) Assertion (A) is false, but Reason (R) is true.

Probability of getting an irrational number at random from the numbers $\sqrt{3}$, $\sqrt{4}$, $3\sqrt{9}$, $3\sqrt{8}$, $\sqrt{5}$, $0$, $4^2$ is:

Assertion (A): The probability that the date of birth of a man is in the month of June is $\frac{1}{12}$
Reason (R) : There are $12$ months in a year.

A bag contains 4 red, 3 blue and 2 yellow balls. One ball is drawn at random from the bag. Find the probability that drawn ball is
(i) red (ii) yellow.

A carton consists of $60$ shirts of which $48$ are good, $8$ have major defects and $4$ have minor defects. Nigam, a trader, will accept the shirts which are good but Anmol, another trader, will only reject the shirts which have major defects. One shirt is drawn at random from the carton. Find the probability that it is acceptable to Anmol.

Two friends Anil and Ashraf were born in the December month in the year $2010$. Find the probability that :
(i) they share same date of birth.
(ii) they have different dates of birth.

A bag contains $25$ balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $\frac{3}{5}$, then find the number of yellow balls.

A box consists of 60 wall clocks, out of which 40 are good, 15 have minor
defects and the remaining are broken. A trader will reject the box, if the
clock taken out from the box is broken. The trader randomly takes out one
clock from the box. What is the probability that :
(i) the box will be rejected ?
(ii) the clock taken out of the box has minor defect ?

Each letter of the word 'MATHEMATICS' is written on separate slips and slips are put in a box and shuffled. A slip is selected at random from the box. Find the probability that the letter written on the slip is :
(i) a vowel,
(ii) either M or T.

A bag contains $10$ red pens, out of which $3$ are defective and $8$ blue pens, out of which $4$ are defective. A pen is taken out from the bag at random. Find the probability that
(i) it is a defective pen,
(ii) it is a non-defective red pen.

If $65\%$ of the population has black eyes, $25\%$ have brown eyes and the remaining have blue eyes, what is the probability that a person selected at random has :
(a) blue eyes?
(b) brown or black eyes?

A lot consists of $200$ pens of which $180$ are good and the rest are defective. A customer will buy a pen if it is not defective. The shopkeeper draws a pen at random and gives it to the customer. What is the probability that the customer will not buy it ? Another lot of $100$ pens containing $80$ good pens is mixed with the previous lot of $200$ pens. The shopkeeper draws one pen at random from the entire lot and gives it to the customer. What is the probability that the customer will buy the pen ?

A lot consists of 200 pens of which 180 are good and the rest are defective. A customer will buy a pen if it is not defective. The shopkeeper draws a pen at random and gives it to the customer. What is the probability that the customer will not buy it ? Another lot of 100 pens containing 80 good pens is mixed with the previous lot of 200 pens. The shopkeeper now draws one pen at random from the entire lot and gives it to the customer. What is the probability that the customer will buy the pen ?

A box contains $6$ blue, $4$ white and $8$ red marbles. A marble is drawn at random from this box. Find the probability that the marble so drawn is :
(i) white
(ii) white or red
(iii) not red

Case Study - 3
Computer-based learning (CBL) refers to any teaching methodology that makes use of computers for information transmission. At an elementary school level, computer applications can be used to display multimedia lesson plans. A survey was done on $1000$ elementary and secondary schools of Assam and they were classified by the number of computers they had.
Number of Computers
Number of Schools
1-10
250
11-20
200
21-50
290
51-100
180
101 and more
80
One school is chosen at random. Then :
(i) Find the probability that the school chosen at random has more than $100$ computers.
(ii) (a) Find the probability that the school chosen at random has $50$ or fewer computers.
OR
(ii) (b) Find the probability that the school chosen at random has no more than $20$ computers.
(iii) Find the probability that the school chosen at random has $10$ or less than $10$ computers.

In a survey on holidays, $120$ people were asked to state which type of transport they used on their last holiday. The following pie chart shows the results of the survey.
Observe the pie chart and answer the following questions :
(i) If one person is selected at random, find the probability that he/she travelled by bus or ship.
(ii) Which is most favourite mode of transport and how many people used it?
(iii) (a) A person is selected at random. If the probability that he did not use train is $4/5$, find the number of people who used train.
OR
(iii) (b) The probability that randomly selected person used aeroplane is $7/60$. Find the revenue collected by air company at the rate of ₹5,000 per person.

The probability for a randomly selected number out of $1, 2, 3, 4, \ldots, 25$ to be a prime number is :

A bag contains $100$ cards numbered $1$ to $100$. A card is drawn at random from the bag. What is the probability that the number on the card is a perfect cube ?

A box contains $90$ discs, numbered from $1$ to $90$. If one disc is drawn at random from the box, the probability that it bears a prime number less than $23$ is

Cards bearing numbers $3$ to $20$ are placed in a bag and mixed thoroughly. A card is taken out of the bag at random. What is the probability that the number on the card taken out is an even number ?

From the data $1, 4, 7, 9, 16, 21, 25$, if all the even numbers are removed, then the probability of getting at random a prime number from the remaining is :

A box contains cards numbered $6$ to $55$. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square, is

If a digit is chosen at random from the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$; then the probability that this digit is an odd prime number is :

One ticket is drawn at random from a bag containing tickets numbered $1$ to $40$. The probability that the selected ticket has a number which is a multiple of $7$ is:

What is the probability that a number selected randomly from the numbers $1, 2, 3, ..., 15$ is a multiple of $4$ ?

Cards numbered $10, 11, 12, \dots, 30$ are kept in a box and shuffled thoroughly. Rohit draws a card at random from the box. The probability that the number on the card is a multiple of $4$ or $5$ is :

The probability of drawing an even prime number out of numbers from $1$ to $30$ is:

The probability of getting a composite number greater than 3 on throwing a die is

The probability that a $2$-digit number less than $20$, selected at random will be a multiple of $2$ and not a multiple of $3$, is

One ticket is drawn at random from a bag containing $50$ tickets numbered $1$ to $50$. The probability that the drawn ticket has a number which is a multiple of $7$ is:

Probability of getting an irrational number at random from the numbers $\sqrt{3}$, $\sqrt{4}$, $3\sqrt{9}$, $3\sqrt{8}$, $\sqrt{5}$, $0$, $4^{\frac{3}{2}}$ is :

A card is drawn from a packet of $50$ identical cards numbered from $1$ to $50$. The probability of drawing a number which is a perfect square, is :

A bag contains cards which are numbered from $5$ to $100$ such that each card bears a different number. A card is drawn at random. Find the probability that number on the card is
(i) a perfect square
(ii) a $2$-digit number

A bag contains balls numbered $2$ to $91$ such that each ball bears a different number. A ball is drawn at random from the bag. Find the probability that (i) it bears a $2$-digit number (ii) it bears a multiple of $1$.

A box contains 120 discs, which are numbered from 1 to 120. If one disc is drawn at random from the box, find the probability that
(i) it bears a 2-digit number
(ii) the number is a perfect square.

A card is drawn at random from a pack of $50$ cards numbered $1$ to $50$. Find the probability of drawing a number which is a perfect square.

A piggy bank contains fifty ₹1 coins, hundred ₹2 coins and one hundred and fifty ₹5 coins. If it is equally likely any one of the coins will fall out when the bank is turned upside down, find the probability that ₹2 coin has not fallen out, when the bank is turned upside down.

Find the probability that a number selected at random from the numbers $30, 31, 32, 33, \text{......}, 60$ is (i) a prime number (ii) a multiple of $6$.

A box contains $90$ discs which are numbered $1$ to $90$. If one disc is drawn at random from the box, find the probability that it bears a :
(i) $2$-digit number less than $40$.
(ii) number divisible by $5$ and greater than $50$.
(iii) a perfect square number.

Rahul is a lucky charm for his cricket team. He has a jar of cards with numbers from $10$ to $74$. Before each match, he draws a card from the jar. If the card bears an even number, the team wins. If the number is even and divisible by $5$, they win by a big margin. If the number is an odd number less than $30$, they win by a small margin. And if the number is a prime number between $50$ and $74$, they lose.
Answer the following questions if Rahul draws a card today:
(i) What is the probability that Rahul draws a card with an even number?
(ii) What is the probability that Rahul draws a card with an odd number less than $30$?
(iii) (a) What is the probability that Rahul draws a card with a prime number between $50$ and $74$?
OR
(b) What is the probability that Rahul draws a card with an even number divisible by $5$?

Which of the following numbers cannot be the probability of happening of an event?

Which of the following is not probability of an event ?

Assertion (A) : If probability of happening of an event is $0.2p$, $p > 0$, then $p$ can't be more than $5$.
Reason (R) : $P(E) = 1 - P(\bar{E})$ for an event $E$.
(a) Both Assertion (A) and Reason (R) are true, and (R) is the correct explanation of (A).
(b) Both Assertion (A) and Reason (R) are true, but (R) is not the correct explanation of (A).
(c) (A) is true, but (R) is false.
(d) (A) is false, but (R) is true.

Which of the following can not be the probability of an event ?

In a random experiment of throwing a die, which of the following is a sure event ?

Assertion (A): The probability of an event can not be $\frac{1}{0.9}$.
Reason (R): $0 \le P(E) \le 1$ for an event E.

Lali tosses two different coins simultaneously. The probability that she gets at most one head is:

If three coins are tossed simultaneously, what is the probability of getting at most one tail?

Two coins are tossed together. The probability of getting at least one tail is:

Two coins are tossed simultaneously. The probability of getting at most one tail is:

The probability of throwing a number greater than $2$ with a fair die is :

Three coins are tossed together. The probability of getting exactly one
nhead, is:

Three coins are tossed together. The probability that only one coin shows tail, is :

Three coins are tossed together. The probability that at least one head comes up, is

If a fair coin is tossed twice, find the probability of getting 'atmost one head'.

Three different coins are tossed together. Find the probability of getting at least two tails.

Three different coins are tossed simultaneously. Find the probability of getting :
(i) At least one head,
(ii) At most two heads.

Three coins are tossed simultaneously. What is the probability of getting
(i) at least one head?
(ii) exactly two tails ?
(iii) at most one tail?

Three unbiased coins are tossed simultaneously. Find the probability of getting :
(i) at least one head.
(ii) exactly one tail.
(iii) two heads and one tail.

Two different coins are tossed simultaneously. What is the probability of getting:
(i) at least one head?
(ii) at most one tail ?
(iii) a head and a tail ?

Three unbiased coins are tossed simultaneously. Find the probability of getting :
(a) exactly two tails
(b) at least one head
(c) at most two heads

A girl calculates that the probability of her winning the first prize in a lottery is $0.08$. If $6000$ tickets are sold, how many tickets has she bought?

A bag contains $5$ red balls and $n$ green balls. If the probability of drawing a green ball is three times that of a red ball, then the value of $n$ is :

The probability of getting a chocolate flavoured ice cream at random, in a lot of $600$ ice creams is $0.055$. The number of chocolate flavoured ice creams in the lot is :

The probability of guessing the correct answer to a certain test question is $\frac{x}{6}$. If the probability of not guessing the correct answer to this question is $\frac{2}{3}$, then the value of $x$ is:

The probability of getting a bad egg in a lot of $400$ eggs is $0.045$. The number of good eggs in the lot is:

The number of red balls in a bag is $10$ more than the number of black balls. If the probability of drawing a red ball at random from this bag is $\frac{3}{5}$, then the total number of balls in the bag is :

Meena calculates that the probability of her winning the first prize in a lottery is $0.08$. If total $800$ tickets were sold, the number of tickets bought by her, is

The probability of guessing the correct answer of a certain test question is $\frac{x}{12}$. If the probability of not guessing the correct answer is $\frac{5}{6}$, then find the value of $x$.

The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is $\frac{12}{23}$, find the total number of balls in the given bag.

A bag contains $40$ marbles out of which some are white and others are black. If the probability of drawing a black marble is $\frac{3}{5}$, then find the number of white marbles.

In a pre-primary class, a teacher put cards numbered $20$ to $59$ in a bowl. A student picked up a card at random and read the number. Find the probability that the number read was (i) a prime number (ii) a perfect square.

A jar contains $54$ marbles, each of which is blue, green or white. The probability of selecting a blue marble at random from the jar is $\frac{1}{3}$, and the probability of selecting a green marble at random is $\frac{4}{9}$. How many white marbles does this jar contain ?

A bag contains $30$ balls out of which '$m$' number of balls are blue in colour.
(i) Find the probability that a ball drawn at random from the bag is not blue.
(ii) If $6$ more blue balls are added in the bag, then the probability of drawing a blue ball will be $\frac{5}{4}$ times the probability of drawing a blue ball in the first case. Find the value of $m$.

A number is chosen from the numbers $1, 2, 3$ and denoted as $x$, and a number is chosen from the numbers $1, 4, 9$ and denoted as $y$. Then $P(xy < 9)$ is:

The total number of outcomes in the experiment of simultaneous throw of three dice is :

Slips of letters of the word 'BACKGROUND' are put in a bowl and thoroughly mixed. One slip is picked up at random. Find the probability that picked up slip's letter is (i) a vowel (ii) present in the word 'BALL'.

A middle school decided to run the following spinner game as a fund-raiser on Christmas Carnival.
Making Purple: Spin each spinner once. Blue and red make purple. So, if one spinner shows Red (R) and another Blue (B), then you 'win'. One such outcome is written as 'RB'.
Based on the above, answer the following questions :
(i) List all possible outcomes of the game.
(ii) Find the probability of 'Making Purple'.
(iii) (a) For each win, a participant gets ₹10, but if he/she loses, he/she has to pay ₹5 to the school. If $99$ participants played, calculate how much fund could the school have collected.
OR
(iii) (b) If the same amount of ₹5 has been decided for winning or losing the game, then how much fund had been collected by school? (Number of participants = $99$)

"Eight Ball" is a game played on a pool table with 15 balls numbered 1 to 15 and a "cue ball" that is solid and white. Of the 15 numbered balls, eight are solid (non-white) coloured and numbered 1 to 8 and seven are striped balls numbered 9 to 15.
The 15 numbered pool balls (no cue ball) are placed in a large bowl and mixed, then one ball is drawn out at random.
Based on the above information, answer the following questions :
(i) What is the probability that the drawn ball bears number 8 ?
(ii) What is the probability that the drawn ball bears an even number?
OR
What is the probability that the drawn ball bears a number, which is a multiple of 3?
(iii) What is the probability that the drawn ball is a solid coloured and bears an even number?

Raghav has a collection of balls of different colours. He has a total of $35$ balls in his basket out of which seven are black in colour and eight are yellow in colour. Out of remaining balls, some are white and the rest are red.
Based on the above, answer the following questions :
(a) If the probability of drawing a red ball at random from the basket is three times that of a white ball, then find the number of red balls in the basket.
(b) Find the probability of drawing a ball at random from the basket which is either a black or a white ball.

Assertion (A): Two players, Sania and Ashnam play a tennis match. The probability of Sania winning the match is $0.79$ and that of Ashnam winning the match is $0.21$.
Reason (R): The sum of probabilities of two complementary events is $1$.

Probability of happening of an event is denoted by $p$ and probability of non-happening of the event is denoted by $q$. Relation between $p$ and $q$ is

If the probability of a player winning a game is $0.79$, then the probability of his losing the same game is :

Assertion (A): In a cricket match, a batsman hits a boundary $9$ times out of $45$ balls he plays. The probability that in a given ball, he does not hit the boundary is $\frac{4}{5}$.
Reason (R): $P(E) + P(\text{not } E) = 1$
(a) Both Assertion (A) and Reason (R) are true, and (R) is the correct explanation of (A).
(b) Both Assertion (A) and Reason (R) are true, but (R) is not the correct explanation of (A).
(c) (A) is true, but (R) is false.
(d) (A) is false, but (R) is true.

For an event $E$, if $P(E) + P(\overline{E}) = q$, then the value of $q^2-4$ is:

Assertion (A): The probability of selecting a number at random from the numbers $1$ to $20$ is $1$. Reason (R): For any event $E$, if $P(E) = 1$, then $E$ is called a sure event.

If for any event E, $P(E) + P(\bar{E}) = q$, then the value of $q^2-3$ is:

In an experiment of throwing a die, Assertion (A): Event $E_1$: getting a number less than 3 and Event $E_2$: getting a number greater than 3 are complementary events. Reason (R): If two events $E$ and $F$ are complementary events, then $P(E) + P(F) = 1$.

A bag contains 3 red, 4 white and 7 green balls. A ball is drawn at random. The probability that the ball drawn is $not$ of red colour is :

Assertion (A) : If $E$ is an event such that $P(E) = \frac{1}{999}$, then $P(\bar{E}) = 0.001$.
Reason (R) : $P(E) + P(\bar{E}) = 1$

If $E$ is an event such that $P(E) = 0.1$, then $P(\bar{E})$ is equal to

If $E$ is an event such that $P(E) = 1\%$, then $P(\overline{E})$ is equal to

If probability of happening of an event is $57\%$, then probability of non-happening of the event is

A bag contains some red and some white balls. A ball is drawn at random from the bag. If the probability of getting a red ball is $\frac{2}{7}$, then the probability of getting a white ball is

In a single throw of two dice, the probability of getting a sum of $10$ is:

In a single throw of two dice, the probability of getting $12$ as a product of two numbers obtained is:

Two dice are thrown together. The probability of getting the difference of numbers on their upper faces equals to $3$ is :

Two dice are rolled together. What is the probability of getting a sum greater than $10$?

Two dice are thrown at the same time and the product of the numbers appearing on them is noted. The probability that the product of the numbers lies between $8$ and $13$ is:

Two dice are rolled together. The probability of getting sum of numbers on the two dice as $2, 3$ or $5$, is :

Two dice are rolled together. The probability of getting the sum of the two numbers to be more than $10$, is

Two dice are thrown together. The probability that they show different numbers is :

Two dice are tossed simultaneously. The probability of getting odd numbers on both the dice is :

The probability of getting a sum of $8$, when two dice are thrown simultaneously, is :

Two dice are thrown simultaneously and the product of the numbers appearing on the tops is noted. The probability of the product to be less than $6$ is:

Two dice are thrown at the same time. The probability that the sum appearing on the tops is $8$, is :

A die is thrown once. The probability of getting a number which is
textbf{not} a factor of $36$, is :

A pair of dice is thrown. The probability that sum of numbers appearing on top faces is at most $10$ is :

A pair of dice is thrown once. The probability that sum of numbers appearing on top faces is at least $4$ is :

Two dice are rolled together. The probability that the sum of the numbers obtained is divisible by $6$, is:

Two different dice are rolled together. The probability that both the obtained numbers are less than $4$, is

Two dice are rolled together. The probability that sum of the numbers obtained is atmost $12$, is

Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x > y$, is

Two dice are thrown simultaneously. The probability of getting a sum of $7$ is:

In an experiment of throwing a pair of dice, the probability of not getting a doublet is :

A pair of dice is thrown simultaneously. Let $E$ denote the event that "The sum of numbers obtained on both dice is at least 9." The number of outcomes in favour of event $E$ is :

Two dice are rolled together. The probability that at least one of them shows a six, is :

Two dice are rolled together. The probability that only one die shows number $4$, is

Two dice are rolled together. The probability of getting a sum more than 9 is

Two dice are rolled together. The probability of getting an outcome $(a, b)$ such that $b = 2a$, is

An unbiased die is thrown once. The probability of getting an even prime number greater than 2 is:

An unbiased die is thrown once. The probability of getting an odd prime number less than $3$ is:

An unbiased die is thrown once. The probability of getting an even multiple of $3$ is:

Assertion (A): The events "getting $2$" and "not getting $2$" in a single throw of an unbiased die are not equally likely events.
Reason (R): The probability of getting $2$ in a single throw of an unbiased die is $\frac{1}{6}$.

The probability of getting sum greater than $10$, when two dice are rolled together, is

The probability of getting a sum of $7$, when two dice are thrown simultaneously, is :

A die is thrown twice. What is the probability that (i) difference between two numbers obtained is 3? (ii) sum of the numbers obtained is 8?

A die is thrown twice. Find the probability that $5$ will come up atleast once.

Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is $2$.

Two dice are rolled together. Find the probability of getting:
(i) a multiple of $2$ on one and a multiple of $3$ on the other die.
(ii) the product of two numbers on the top of the two dice is a perfect square number.

Two dice of different colours are thrown at the same time. Write down all the possible outcomes. What is the probability that :
(i) same number appears on both the dice ?
(ii) different number appears on both the dice ?

Two dice are thrown at the same time. Determine the probability that the (i) sum of the numbers on the two dice is $5$, and (ii) difference of the numbers on the two dice is $3$.

Two different dice are thrown together. Find the probability that the numbers obtained have :
(i) even sum,
(ii) even product.

Two dice are rolled together. Find the probability that :
(i) the sum of the numbers obtained is 10.
(ii) the product of the numbers obtained is 6.

Two dice are rolled together. Find the probability that at least one of the numbers obtained is a multiple of $3$.

Two dice are rolled together. Find the probability that (i) in the obtained outcomes one number is twice the another. (ii) both the numbers obtained are greater than $4$.

A card is drawn at random from a well-shuffled pack of $52$ cards. The probability that the card drawn is not an ace is :

One card is drawn at random from a well shuffled pack of $52$ playing cards. The probability that the drawn card is a queen, is :

A card is drawn at random from a well shuffled deck of 52 playing cards. The probability of getting a face card is

All queens, jacks and aces are removed from a pack of $52$ playing cards. The remaining cards are well-shuffled and one card is picked up at random from it. The probability of that card to be a king is :

One card is drawn at random from a well shuffled deck of 52 playing cards. The probability that it is a red ace card, is :

A card is selected at random from a deck of $52$ playing cards. The probability of it being a red face card is:

A card is drawn at random from a pack of $52$ cards. What is the probability that the card drawn is a spade or a king?

If all the red face cards are removed from the deck of $52$ playing cards, then the probability of getting a black jack from the remaining cards is :

A card is drawn at random from a deck of $52$ playing cards. The probability that the drawn card is not a red face card, is

A card is drawn at random from a well shuffled deck of 52 playing cards. The probability that it is either a ten or a king is

A card is drawn at random from a well shuffled deck of $52$ playing cards. The probability that drawn card shows number '9' is :

A black card is lost from a deck of $52$ playing cards. Rest of the cards are shuffled and one card is drawn at random from the available cards. The probability that drawn card is 'king of hearts', is

A card is drawn from a well shuffled deck of 52 cards. The probability of getting an ace or a ten is:

A card is drawn from a well shuffled deck of $52$ cards. The probability that it is not a diamond card is :

A card is drawn from a well-shuffled deck of $52$ playing cards. The probability of getting a queen of spade is

In a pack of $52$ playing cards one card is lost. From the remaining cards, a card is drawn at random. Find the probability that the drawn card is queen of heart, if the lost card is a black card.

One card is drawn at random from a well shuffled deck of $52$ cards. Find the probability that the card drawn
(i) is queen of hearts;
(ii) is not a jack.

This section comprises Very Short Answer (VSA) type questions of $2$ marks each
The king, queen and ace of clubs and diamonds are removed from a deck of $52$ playing cards and the remaining cards are shuffled. A card is randomly drawn from the remaining cards. Find the probability of getting
(i) a card of clubs.
(ii) a red coloured card.

From a pack of $52$ playing cards, jack, queen and king of diamonds are removed. A card is drawn at random from the remaining cards. Find the probability of getting a face card or a card of spades.

While shuffling a pack of 52 cards, one card was accidentally dropped. Find the probability that the dropped card (i) is not a face card. (ii) is a black king.

All the face cards are removed from the pack of 52 cards and a card is drawn at random from the remaining cards. Find the probability that the card so drawn is
(i) a spade.
(ii) not an ace.

From a pack of $52$ cards, all aces and all kings are removed. A card is drawn at random from the remaining cards. Find the probability that the card so drawn is (i) a face card. (ii) a card of red colour.

All the red face cards are removed from a pack of $52$ playing cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting a :
(i) red card
(ii) a king or queen

All face cards of spades are removed from a pack of $52$ playing cards and the remaining pack is shuffled well. A card is then drawn at random from the remaining pack. Find the probability of getting :
(a) a face card
(b) an ace or a jack

A group of friends wanted to play cards with two identical packs together. While shuffling the cards, three cards are dropped. Rest of the cards are shuffled and one card is drawn at random. Assuming that the dropped cards were a queen of hearts, a ten of spades and an ace of clubs, answer the following questions:
(i) Find the probability that the drawn card is a face card.
(ii) Find the probability that the drawn card is either a king or a queen.
(iii) (a) Do you think that the probability of getting a queen was higher if none of the cards were dropped? Justify your answer.
OR
(iii) (b) Find the probability that the drawn card is a jack. Compare it with the probability when none of the cards were dropped. In which case is the probability of getting a jack higher?

A group of friends wanted to play cards with two identical packs together.
nWhile shuffling the cards, three cards are dropped. Rest of the cards are
nshuffled and one card is drawn at random. Assuming that the dropped
ncards were a queen of hearts, a ten of spades and an ace of clubs, answer
nthe following questions :
n(i) Find the probability that the drawn card is a face card.
n(ii) Find the probability that the drawn card is either a king or a
nqueen.
n(iii) (a) Do you think that the probability of getting a queen was
nhigher if none of the cards were dropped? Justify your
nanswer.
nOR
n(iii) (b) Find the probability that the drawn card is a jack. Compare
nit with the probability when none of the cards were dropped.
nIn which case is the probability of getting a jack higher?