CUET · MATHS · PYQ PAPER 2025
In a game, a man wins ₹ \( 8\) for getting a number greater than 3 and loses ₹ 3 otherwise, when a fair die is thrown.
The man decided to throw a die 4 times but to quit as and when he gets a number greater than 3.
If \(X\) denotes the amount which the man wins or loses, then which of the following are correct?
(A) All the possible values of \(X\) are \(8,5,2\) and -1 .
(B) The probability distribution of \(X\) is :
| X | 8 | 5 | 2 | -1 | -12 |
| P(X) | 1/2 | 1/4 | 1/8 | 1/16 | 1/16 |
(C) The mean value of \(X\) is \(\frac{75}{16}\).
(D) The variance of \(X\) is \(\frac{6615}{256}\).
Choose the correct answer from the options given below :
- A A) and (B) only
- B (A), (B) and (C) only
- C (B), (C) and (D) only
- D (C) and (D) only
Answer & Solution
Correct Answer
(C) (B), (C) and (D) only
Step-by-step Solution
Detailed explanation
\(P(\text{win}) = \frac{3}{6} = \frac{1}{2}\) \(P(\text{lose}) = \frac{3}{6} = \frac{1}{2}\) Possible values of \(X\): \(X=8\): Win on 1st throw. \(P(X=8) = \frac{1}{2}\). \(X=5\): Lose, then Win. (\(-3+8\)). \(P(X=5) = \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}\). \(X=2\):…
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