Question

Choose the correct option from the given alternatives:

The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

Options

• `128/256`

• `219/256`

• `37/256`

• `28/256`

Answer 1

`28/256`

Explanation:

np = 4, npq = 2

∴ q = `1/2` and p = `1/2`

∴ `"n"(1/2) = 4`

∴ n = 8

∴ P(X = 2) = `"^8C_2 (1/2)^8 = (8 xx 7)/(1 xx 2) xx 1/256 = 28/256`