Probability — Class 10 Maths PYQs

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

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

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?

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

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 :

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 :

Cards numbered 10, 11, 12, ..., 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

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 $90$ 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 ?

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 :

Two coins are tossed simultaneously. The probability of getting atleast one head 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.

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 :

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 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 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:

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?

Questions number $19$ and $20$ are Assertion and Reason based questions carrying $1$ mark each. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.
(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): 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

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): $P(E) + P(\text{not } E) = 1$

Directions : Questions number $19$ and $20$ are Assertion and Reason based questions carrying $1$ mark each. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (A), (B), (C) and (D) as given below:
(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): 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): $P(E) + P(\text{not } E) = 1$

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

For an event E, if $P(E) + P(\bar{E}) = q$, 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.

Questions number $19$ and $20$ are Assertion and Reason based questions. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (A), (B), (C) and (D) as given below.
(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 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 $P(E) + P(F) = 1$.

Assertion (A): A fair die is thrown once. The probability of getting a prime number is $\frac{1}{2}$.
Reason (R): A natural number is a prime number if it has only two factors.

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 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 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 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.

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

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 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