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Probability - ISC Class 12 Mathematics Questions with Answers

92 past-paper questions on Probability from ISC Class 12 Mathematics papers (2027-2017), newest first. Open one to see its answer.

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The probability distribution of random variable X is given below: X 1 2 3 4 5 P(X) m 3m a 5m b If $P(X \le 2) = 0.28$ and… 2027 · 1 mark · Short answer
In a game show, a contestant is shown three closed doors: Door A, Door B and Door C. Behind one door is a laptop while the other… 2027 · 5 marks · Short answer
If $P(A) = m$, $P(B/\bar{A}) = 3m$, $P(B/A) = 6m$, then what will be $P(A/B)$? 2027 · 1 mark · MCQ
In a large organisation, only 1 out of every 1,500 emails contains a harmful attachment. An automated filtering system is used to… 2027 · 5 marks · Short answer
In a school, for a period of 8 working days, it is equally likely that Tanishka is present or absent on any given day. What is… 2027 · 2 marks · Short answer
Three friends go to a restaurant to have pizza. They decide who will pay for the pizza by tossing a coin. It is decided that each… 2026 · 4 marks · Short answer
A die marked 1, 2, 3 in red and 4, 5, 6 in green is thrown. Let A be the event 'Number appearing is odd' and B be the event… 2026 · 2 marks · Derivation
A school conducted an inter house quiz competition. The number of students who participated in the competition was 15. The scores… 2026 · 6 marks · Case based
A gardener wants to plant saplings on a day when rain is not predicted. According to the forecast by the weather department, -… 2026 · 6 marks · Case based
A school offers students the choice of three modes for attending classes: • Mode A: Offline (in-person) – 40% of students • Mode… 2026 · 4 marks · Short answer
In a school, three subject teachers English, Math, and Science sometimes give surprise tests on the same day. Based on past… 2026 · 6 marks · Short answer
A football club purchased footballs manufactured at three different factories in Chennai, Mumbai and Delhi. Given below is the… 2026 · 4 marks · Numerical
Children of a society practise building human pyramids for 16 days to participate in the pyramid building competition during the… 2026 · 4 marks · Case based
If $A$ and $B$ are two independent events such that $P(A \cup B) = \frac{3}{5}$ and $P(A) = \frac{1}{2}$, calculate $P(B)$. 2026 · 2 marks · Numerical
A die is thrown three times. If the first throw is a four, then the probability of getting 15 as a sum is: 2026 · 1 mark · MCQ
If events $A$ and $B$ are mutually exclusive, such that $P(A) = \frac{1}{5}$ and $P(B) = \frac{2}{3}$, then the value of… 2026 · 1 mark · MCQ
A sports store owner conducts a game 'weekend-surprise' every Friday for his customers. He fills two bags with cricket balls of… 2026 · 4 marks · Short answer
Students of under graduation submitted a case study on “Understanding the Probability of Left-Handedness in Children Based on… 2025 · 4 marks · Case based
In a class of 50 students, 25 study English, 10 study History and 10 study both the subjects. Find the probability that a… 2025 · 1 mark · Short answer
Ram and Shyam play a game with a coin. Ram stakes ₹ 1.00 and throws the coin 4 times. If he throws 4 heads, he gets his stake and… 2025 · 6 marks · Long answer
Rahul and Divya were playing the snakes and ladders board game. Each one had their own dice to play the game. Rahul was using a… 2025 · 4 marks · Long answer
For any given events A: Statement I: Event A and null event $\emptyset$ are always independent. Statement II: Event A and sure… 2025 · 1 mark · MCQ
Three fair dice are thrown. What is the probability of getting a total of 15 given that they exhibit three different numbers that… 2025 · 1 mark · MCQ
In a raffle draw, 1000 raffle tickets are sold for ₹ 1 each. Each has an equal chance of winning. First prize is ₹ 300, second… 2025 · 6 marks · Long answer
A biased dice is tossed and the respective probabilities for various faces to turn up are: Face 1 2 3 4 5 6 Probability 0.10 0.24… 2025 · 1 mark · Short answer
Pia, Sia and Dia displayed their paintings in an art exhibition. The three artists displayed $15$, $5$ and $10$ of their… 2025 · 4 marks · Short answer
Consider the two events $A$ and $B$. The probability that at least one of $A$ or $B$ occurs is $0\cdot 6$. If the probability of… 2025 · 1 mark · Numerical
If $E_1$ and $E_2$ are two mutually exclusive events associated with a random experiment and $E$ is an event such that… 2025 · 1 mark · Assertion-reason
An international conference takes place in a metropolitan city. International leaders, scientists and industrialists participate… 2025 · 6 marks · Short answer
A pot contains 5 red and 2 green balls. At random a ball is drawn from this pot. If a drawn ball is green, then put a red ball in… 2025 · 4 marks · Short answer
Three friends go to a restaurant to have pizza. They decide who will pay for the pizza by tossing a coin. It is decided that each… 2025 · 4 marks · Short answer
Let $X$ be a discrete random variable. The probability distribution of $X$ is given below: $X$ $30$ $10$ $-10$ $P(X)$… 2025 · 1 mark · MCQ
In an examination, a candidate takes three tests namely $\alpha, \beta, \gamma$ in succession and the probability of failing the… 2025 · 1 mark · MCQ
If $A$ and $B$ are two events such that $P(\bar{A}) = 0.3$, $P(B) = 0.4$, $P(A \cap \bar{B}) = 0.5$, then find the value of… 2025 · 1 mark · Short answer
Consider the two events $A$ and $B$ such that $n(A) = n(B)$ and $P(A/B) = P(B/A)$. 2025 · 1 mark · Assertion-reason
Three critics review a book. Odds in favour of the book are $5:2$, $4:3$ and $3:4$ respectively for the three critics. Find the… 2025 · 1 mark · Numerical
Rohit and Vishal, two below-average students in a class, are attempting a Mathematics problem during revision classes. Their… 2025 · 1 mark · MCQ
Kiran plays a game of throwing a fair die 3 times but to quit as and when she gets a six. Kiran gets +1 point for a six and −1… 2025 · 6 marks · Short answer
There are 10 cookies in a box. Six have chocolate centres and four have jam-filled centres. Shweta randomly chooses a cookie from… 2025 · 1 mark · Short answer
If $P(A) = \frac{1}{2}, P(B) = \frac{1}{3}$ and $P(A \cup B) = \frac{2}{3}$, then the value of $P(A|B) + P(B|A)$ is: 2025 · 1 mark · MCQ
Rahul, a class XII student, has a probability of getting a grade A in the examination of three subjects namely Mathematics… 2025 · 1 mark · Short answer
In a school, there are 30 teachers in the examination committee. Out of these, 20 never commit any error in their work. Two… 2025 · 4 marks · Short answer
Naman has to attend his friend's marriage. He can reach the wedding venue by train, bus or a two-wheeler. The probability of… 2025 · 6 marks · Short answer
In a Kabaddi league, two matches are being played between Jaipur and Delhi. It is assumed that the outcomes of two games are… 2025 · 4 marks · Long answer
A primary school teacher wants to teach the concept of 'larger number' to the students of Class II. To teach this concept, he… 2024 · 6 marks · Short answer
Evaluate: $P(A \cup B)$ if $2P(A) = P(B) = \frac{5}{13}$ and $P(A|B) = \frac{2}{5}$ 2024 · 2 marks · Numerical
Teena is practising for an upcoming Rifle Shooting tournament. The probability of her shooting the target in the $1^{\text{st}}$… 2024 · 1 mark · Short answer
A jewellery seller has precious gems in white and red colour which he has put in three boxes. The distribution of these gems is… 2024 · 4 marks · Numerical
A biased four-sided die with faces labelled 1, 2, 3 and 4 is rolled and recorded. Let $X$ be the result obtained when the die is… 2023 · 6 marks · Long answer
The probability of the event $A$ occurring is $\frac{1}{3}$ and of the event $B$ occurring is $\frac{1}{2}$. If $A$ and $B$ are… 2023 · 2 marks · Numerical
A candidate takes three tests in succession and the probability of passing the first test is $\frac{1}{2}$. The probability of… 2023 · 4 marks · Short answer
$50$ tickets in a box are numbered $00, 01, 02, \dots, 49$. One ticket is drawn randomly from the box. Find the probability of… 2023 · 1 mark · Short answer
A bag contains 19 tickets, numbered from 1 to 19. Two tickets are drawn randomly in succession with replacement. Find the… 2023 · 1 mark · Numerical
A student answers a multiple choice question with $5$ alternatives, of which exactly one is correct. The probability that he… 2023 · 4 marks · Short answer
A box contains 30 fruits, out of which 10 are rotten. Two fruits are selected at random one by one without replacement from the… 2023 · 6 marks · Short answer
A speaks truth in $60\\%$ of cases and B speaks truth in $90\\%$ of the cases. In what percentage of cases are they likely to… 2023 · 1 mark · Short answer
A problem in Mathematics is given to three students A, B and C. Their chances of solving the problem are $\frac{1}{2}$… 2023 · 4 marks · Short answer
In a company, 15% of the employees are graduates and 85% of the employees are non-graduates. As per the annual report of the… 2023 · 4 marks · Short answer
If $A$ and $B$ are two events such that $P(A) > 0$ and $P(B) \neq 1$, then $P(\bar{A}/\bar{B})$ is 2023 · 1 mark · MCQ
A bag contains 6 red and 5 blue balls and another bag contains 5 red and 8 blue balls. A ball is drawn from the first bag and… 2022 · 4 marks · Short answer
In a bolt factory, machines X, Y and Z manufacture 20%, 35% and 45% respectively of the total output. Of their output 8%, 6% and… 2022 · 6 marks · Short answer
Two cards are drawn out randomly from a pack of 52 cards one after the other, without replacement. The probability of first card… 2022 · 1 mark · MCQ
A bag contains 3 red and 4 white balls and another bag contains 2 red and 3 white balls. If one ball is drawn from the first bag… 2022 · 4 marks · Short answer
If two balls are drawn from a bag containing 3 white, 4 black and 5 red balls. Then, the probability that the drawn balls are of… 2022 · 1 mark · MCQ
$A$ and $B$ appeared for an interview for two vacancies. The probability of $A$’s selection is $\frac{4}{5}$ and $B$’s selection… 2021 · 1 mark · Short answer
A word consists of 10 different alphabets, in which there are 4 consonants and 6 vowels. Four alphabets are chosen at random… 2021 · 4 marks · Short answer
Bag A contains 4 white balls and 3 black balls, while Bag B contains 3 white balls and 5 black balls. Two balls are drawn from… 2021 · 4 marks · Short answer
If $A$ and $B$ are independent events such that $P(A) = 1/4$ and $P(B) = 2/3$. Find $P(A \cap B)$. 2021 · 1 mark · Short answer
Given three identical Boxes A, B and C, Box A contains 2 gold and 1 silver coin, Box B contains 1 gold and 2 silver coins and Box… 2021 · 6 marks · Short answer
If $P(A) = \frac{4}{5}$ and $P(A \cap B) = \frac{7}{10}$, then the value of $P(B/A)$ is: 2021 · 1 mark · MCQ
A bag contains 5 white, 7 red and 4 black balls. If four balls are drawn one by one with replacement, what is the probability… 2020 · 2 marks · Short answer
The probability that a bulb produced in a factory will fuse after 150 days of use is $0.05$. Find the probability that out of 5… 2020 · 6 marks · Short answer
Three persons A, B and C shoot to hit a target. Their probabilities of hitting the target are $\frac{5}{6}$, $\frac{4}{5}$ and… 2020 · 4 marks · Short answer
Let $A$ and $B$ be two events such that $P(A) = \frac{1}{2}$, $P(B) = p$ and $P(A \cup B) = \frac{3}{5}$, find ‘$p$’ if $A$ and… 2020 · 2 marks · Numerical
If events $A$ and $B$ are independent, such that $P(A) = \frac{3}{5}$, $P(B) = \frac{2}{3}$, find $P(A \cup B)$. 2019 · 2 marks · Short answer
Two balls are drawn from an urn containing 3 white, 5 red and 2 black balls, one by one without replacement. What is the… 2019 · 2 marks · Short answer
Given three identical Boxes A, B and C, Box A contains 2 gold and 1 silver coin, Box B contains 1 gold and 2 silver coins and Box… 2019 · 6 marks · Numerical
Determine the binomial distribution where mean is 9 and standard deviation is $\frac{3}{2}$. Also, find the probability of… 2019 · 6 marks · Numerical
Bag A contains 4 white balls and 3 black balls, while Bag B contains 3 white balls and 5 black balls. Two balls are drawn from… 2019 · 4 marks · Numerical
Let $X$ denote the number of hours you study during a randomly selected school day. The probability that $X$ can take the values… 2018 · 4 marks · Short answer
From a lot of 6 items containing 2 defective items, a sample of 4 items are drawn at random. Let the random variable $X$ denote… 2018 · 6 marks · Short answer
A family has two children. What is the probability that both children are boys, given that at least one of them is a boy? 2018 · 2 marks · Short answer
$A$ speaks truth in $60\%$ of the cases, while $B$ in $40\%$ of the cases. In what percent of cases are they likely to contradict… 2018 · 4 marks · Short answer
In a race, the probabilities of $A$ and $B$ winning the race are $\frac{1}{3}$ and $\frac{1}{6}$ respectively. Find the… 2018 · 2 marks · Short answer
Given that the events $A$ and $B$ are such that $P(A) = \frac{1}{2}$, $P(A \cup B) = \frac{3}{5}$ and $P(B) = k$. Find $k$ if… 2018 · 2 marks · Short answer
A, B and C throw a die one after the other in the same order till one of them gets a '6' and wins the game. Find their respective… 2018 · 6 marks · Long answer
If $A$ and $B$ are events such that $P(A) = \frac{1}{2}$, $P(B) = \frac{1}{3}$ and $P(A \cap B) = \frac{1}{4}$, then find… 2018 · 2 marks · Short answer
A fair die is rolled. If face 1 turns up, a ball is drawn from Bag A. If face 2 or 3 turns up, a ball is drawn from Bag B. If… 2017 · 5 marks · Short answer
Bag A contains 1 white, 2 blue and 3 red balls. Bag B contains 3 white, 3 blue and 2 red balls. Bag C contains 2 white, 3 blue… 2017 · 5 marks · Short answer
A problem is given to three students whose chances of solving it are $\frac{1}{4}, \frac{1}{5}$ and $\frac{1}{3}$ respectively… 2017 · 3 marks · Short answer
In a class of 60 students, 30 opted for Mathematics, 32 opted for Biology and 24 opted for both Mathematics and Biology. If one… 2017 · 5 marks · Short answer
An urn contains 25 balls of which 10 balls are red and the remaining green. A ball is drawn at random from the urn, the colour is… 2017 · 5 marks · Short answer

Probability - ISC Class 12 Mathematics Questions with Answers

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