Question

A six faced die is biased such that
3 × P (a prime number) = 6 × P (a composite number) = 2 × 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. $\frac{8}{11}$

Answer 1

Answer: (D)

$\frac{8}{11}$

Answer 2

The correct answer is (D) : $\frac{8}{11}$
Let P(a prime number) = α
P(a composite number) = β
and P(1) = γ
$∵ 3α = 6β = 2γ = k(say)$
and $3α + 2β + γ = 1$
$⇒ k + \frac{k}{3} + \frac{k}{2} = 1$
$⇒ k = \frac{6}{11}$
Mean = np where n = 2
and p = probability of getting perfect square
$= P(1)+P(4) = \frac{k}{2}+\frac{k}{6} = \frac{4}{11}$
so ,mean $= 2.(\frac{4}{11})$
$= \frac{8}{11}$