JEE Main · 2022 · 27 Jul 2022 · Shift 2 · Probability

A six faced die is biased such that

3 \times P (a prime number) = 6 \times P (a composite number) = 2 \times P (1)

. Let X be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of X is :

(A) $\frac{3}{11}$
(B) $\frac{5}{11}$
(C) $\frac{7}{11}$
(D) $\frac{8}{11}$ ✓ Correct

Answer: (D)

Solution

Let

\frac{P ( prime )}{2} = \frac{P ( composite )}{1} = \frac{P ( 1 )}{3} = k

. Then

P (prime) = 2 k

P (composite) = k

P (1) = 3 k

. Since there are 3 primes (2,3,5), 2 composites (4,6), and one 1:

3 (2 k) + 2 (k) + 3 k = 1

, giving

k = 1/11

. The probability of getting a perfect square (1 or 4) is

P (success) = 3 k + k = 4 k = 4/11

. For

n = 2

trials, mean

= n p = 2 \times \frac{4}{11} = \frac{8}{11}

JEE Main · 2022 · 27 Jul 2022 · Shift 2 · Single correct option

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JEE Main · 2022 · 27 Jul 2022 · Shift 2 · Probability

Solution

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