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

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

TestHub · Accepted Answer

Let P a prime number 2 = P a composite number 1 = P 1 3 = k So, P (a prime number) = 2 k , P (a composite number) = k , and P 1 = 3 k i.e. 6 k + 2 k + 3 k = 1 ⇒ k = 1 11 P ( success ) = P 1 or 4 = 3 k + k = 4 11 Number of trials, n = 2 ∴ required mean = n p = 2 × 4 11 = 8 11

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