CBSE Maths › Class 12 PYQs › Probability

Probability: 5 marks Questions (CBSE Class 12)

2 different 5 marks questions on Probability from CBSE Class 12 Maths board exams 2022–2026, newest first.

1 mark (41)2 marks (16)3 marks (41)4 marks (28)5 marks (2)

Q355 marksLong AnswerProbability CBSE 2023 · 65/5/1

In answering a question on a multiple choice test, a student either knows the answer or guesses. Let $\frac{3}{5}$ be the probability that he knows the answer and $\frac{2}{5}$ be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability $\frac{1}{3}$ . What is the probability that the student knows the answer, given that he answered it correctly ?

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Answer:

\frac{9}{11}

Let $E_{1}$ : student knows the answer, $E_{2}$ : student guesses, A: answer is correct.
$P (E_{1}) = \frac{3}{5}$ , $P (E_{2}) = \frac{2}{5}$ , $P (A ∣ E_{1}) = 1$ , $P (A ∣ E_{2}) = \frac{1}{3}$ .
By Bayes' theorem, $P (E_{1} ∣ A) = \frac{\frac{3}{5} \times 1}{\frac{3}{5} \times 1 + \frac{2}{5} \times \frac{1}{3}} = \frac{\frac{3}{5}}{\frac{11}{15}}$ .
$= \frac{9}{11}$ .

Also asked in: 2023 65/5/2, 2023 65/5/3

Q35 (OR) (OR)5 marksLong AnswerProbability CBSE 2023 · 65/5/1Not in current syllabus

A box contains 10 tickets, 2 of which carry a prize of ₹ 8 each, 5 of which carry a prize of ₹ 4 each, and remaining 3 carry a prize of ₹ 2 each. If one ticket is drawn at random, find the mean value of the prize.

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Answer: ₹ 4.20

Let X be the prize. X takes values 8, 4, 2 with probabilities $\frac{2}{10}$ , $\frac{5}{10}$ , $\frac{3}{10}$ .
Mean $= 8 \times \frac{2}{10} + 4 \times \frac{5}{10} + 2 \times \frac{3}{10} = \frac{16 + 20 + 6}{10}$ .
$= \frac{42}{10} = 4.2$ , i.e. ₹ 4.20.

Also asked in: 2023 65/5/2, 2023 65/5/3

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