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Probability - ISC Class 12 Mathematics Questions with Answers, Page 2

92 past-paper questions on Probability from ISC Class 12 Mathematics papers (2027-2017), newest first, in full. Questions 21-40 are on this page, 20 to a page. Tap "Show answer" under a question to see its answer.

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2025 · 4 marks · Long answerOpen: Rahul and Divya were playing the snakes and ladders board game. Each one had…
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 red dice, whereas Divya was using a black dice. In the beginning of the game, they were using their own dice to play. After some time, in order to play the game faster they both started using both the dice together for playing. When Divya rolled both red and black dice together then:
(a)
find the conditional probability of obtaining sum greater than 9, given that black dice resulted in a 5.
(b)
find the conditional probability that sum of the number on the dice is not 4, given that the numbers on the both the dice are different.

No answer yet.

2025 · 1 mark · MCQOpen: For any given events A: Statement I: Event A and null event are always…
For any given events A: Statement I: Event A and null event $\emptyset$ are always independent. Statement II: Event A and sure event S are always independent.
  • (a)Both the statements are true.
  • (b)Both the statements are false.
  • (c)Statement I is false, and statement II is true.
  • (d)Statement I is true, and statement II is false.

No answer yet.

2025 · 6 marks · Long answerOpen: In a raffle draw, 1000 raffle tickets are sold for ₹ 1 each. Each has an equal…
In a raffle draw, 1000 raffle tickets are sold for ₹ 1 each. Each has an equal chance of winning. First prize is ₹ 300, second prize is ₹ 200, and third prize is ₹ 100. Let X denote the net gain from the purchase of one ticket.
(a)
Construct the probability distribution of X.
(b)
Find the probability of winning any money in the purchase of one ticket.
(c)
Find the expected value of X and interpret its meaning.

No answer yet.

2025 · 4 marks · Short answerOpen: Pia, Sia and Dia displayed their paintings in an art exhibition. The three…
Pia, Sia and Dia displayed their paintings in an art exhibition. The three artists displayed $15$, $5$ and $10$ of their paintings respectively. A person bought three paintings from the exhibition.
(i)[2.0]
Find the probability that he bought one painting from each of them.
(ii)[2.0]
Find the probability that he bought all the three paintings from the same person.

No answer yet.

2025 · 1 mark · Assertion-reasonOpen: If and are two mutually exclusive events associated with a random experiment…

Assertion: If $E_1$ and $E_2$ are two mutually exclusive events associated with a random experiment and $E$ is an event such that $P(E) \neq 0$, then $P\left(\frac{E_1 \cup E_2}{E}\right) = P\left(\frac{E_1}{E}\right) + P\left(\frac{E_2}{E}\right)$.

Reason: For two mutually exclusive events $E_1$ and $E_2$, $P(E_1 \cap E_2) = 0$.

If $E_1$ and $E_2$ are two mutually exclusive events associated with a random experiment and $E$ is an event such that: $P(E) \neq 0$. Assertion (A): $P\left(\frac{E_1 \cup E_2}{E}\right) = P\left(\frac{E_1}{E}\right) + P\left(\frac{E_2}{E}\right)$. Reason (R): For two mutually exclusive events $E_1$ and $E_2$, $P(E_1 \cap E_2) = 0$.
  • (a)Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation for Assertion (A).
  • (b)Both Assertion (A) and Reason (R) are true, but Reason (A) is not the correct explanation for Assertion (A).
  • (c)Assertion (A) is true, and Reason (R) is false.
  • (d)Assertion (A) is false, and Reason (R) is true.

No answer yet.

2025 · 6 marks · Short answerOpen: An international conference takes place in a metropolitan city. International…
An international conference takes place in a metropolitan city. International leaders, scientists and industrialists participate in it. The organisers of the conference appoint three agencies namely X, Y and Z for the security of the participants. The track record of the success of X, Y and Z in providing security services is 99%, 98.5% and 98% respectively. The organisers assign the responsibility of ensuring the security of 1000 people to agency X, 2000 people to agency Y and 3000 people to agency Z. At the end of the conference, one participant goes missing from the conference room. What is the probability that the missing participant was placed under the responsibility of the security agency X?

No answer yet.

2025 · 4 marks · Short answerOpen: A pot contains 5 red and 2 green balls. At random a ball is drawn from this…
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 the pot. If a drawn ball is red, then put a green ball in the pot. While drawn ball is not replaced in the pot. Now, we draw another ball randomly. What is the probability that the second ball drawn is a red ball?

No answer yet.

2025 · 4 marks · Short answerOpen: Three friends go to a restaurant to have pizza. They decide who will pay for…
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 one of them will toss a coin and if one person gets a different result (heads or tails) than the other two, that person would pay. If all three get the same result (all heads or all tails), they will toss again until they get a different result. [Analysis]
(a)
What is the probability that all three friends will get the same result (all heads or all tails) in one round of tossing?
(b)
What is the probability that they will get a different result in one round of tossing?
(c)
What is the probability that they will need exactly four rounds of tossing to determine who would pay?

No answer yet.

2025 · 1 mark · MCQOpen: In an examination, a candidate takes three tests namely in succession and the…
In an examination, a candidate takes three tests namely $\alpha, \beta, \gamma$ in succession and the probability of failing the first test $\alpha$ is $\frac{1}{2}$. The probability of passing each succeeding test is $\frac{1}{2}$ or $\frac{1}{4}$ according to whether he passes or fails in the preceding one. The candidate is selected, if he passes at least two tests. What is the probability that candidate is selected?
  • (a)$\frac{3}{8}$
  • (b)$\frac{1}{8}$
  • (c)$\frac{5}{8}$
  • (d)$\frac{3}{4}$

No answer yet.

2025 · 1 mark · Assertion-reasonOpen: Consider the two events and such that and .

Assertion: Consider the two events $A$ and $B$ such that $n(A) = n(B)$ and $P(A/B) = P(B/A)$.

Reason: The events $A$ and $B$ are mutually exclusive.

  • (a)Both Assertion and Reason are true and Reason is the correct explanation for Assertion.
  • (b)Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.
  • (c)Assertion is true and Reason is false.
  • (d)Assertion is false and Reason is true.

No answer yet.

2025 · 1 mark · MCQOpen: Rohit and Vishal, two below-average students in a class, are attempting a…
Rohit and Vishal, two below-average students in a class, are attempting a Mathematics problem during revision classes. Their respective probabilities of solving the sum correctly are $\frac{1}{6}$ and $\frac{1}{8}$ respectively. Their previous experience shows that while solving the same question, the probability of a common mistake is $\frac{1}{10}$. What is the probability that they obtain the same answer?
  • (a)$\frac{3}{4}$
  • (b)$\frac{7}{48}$
  • (c)$\frac{11}{96}$
  • (d)$\frac{9}{96}$

No answer yet.

2025 · 6 marks · Short answerOpen: Kiran plays a game of throwing a fair die 3 times but to quit as and when she…
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 for any other number. [Analysis]
Figure for this question
(i)
If X denotes the random variable “points earned” then what are the possible values X can take?
(ii)
Find the probability distribution of this random variable X.
(iii)
Find the expected value of the points she gets.

No answer yet.

2025 · 1 mark · Short answerOpen: There are 10 cookies in a box. Six have chocolate centres and four have…
There are 10 cookies in a box. Six have chocolate centres and four have jam-filled centres. Shweta randomly chooses a cookie from the box and eats it. Then, Ali randomly chooses and eats one of the remaining cookies. What is the probability that Shweta and Ali choose cookies with different centres?

No answer yet.

2025 · 1 mark · MCQOpen: If and , then the value of is:
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:
  • (a)$\frac{5}{12}$
  • (b)$\frac{7}{12}$
  • (c)$\frac{5}{6}$
  • (d)$\frac{1}{3}$

No answer yet.

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