Probability — Class 10 Maths PYQs

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?

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 :

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 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

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.

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.

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 ?

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.

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

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

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

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 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.

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

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

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?

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 :

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.

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 $m$.

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

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 $1$.

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:

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

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 :

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

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 $\frac{1}{6}$.

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 ?

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 :

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 :

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 that it is not a diamond card is :

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?