Question

If the mean and variance of a binomial variate X are 14 and 10 respectively, then the probability that X takes a value greater than or equal to 1 is ______

Options

• `(2^47 - 1)/(2^47)`

• `1/2^49`

• `1/2^47`

• `(2^49 - 1)/(2^49)`

Answer 1

If the mean and variance of a binomial variate X are 14 and 10 respectively, then the probability that X takes a value greater than or equal to 1 is `underline((2^49 - 1)/(2^49))`.

Explanation:

We have, mean = np = 14

and variance = npq = 10

∴ `(npq)/(np) = q = 10/14 = 5/7`

∴ p = `2/7` and n = 49

∴ P(X ≥ 1) = 1 - P(X = 0)

= `1 - ""^49"C"_0(1/2)^49`

= `(2^49 - 1)/(2^49)`