Question

Solve the following problem :

Let X ∼ B(10,0.2). Find P(X = 1)

Answer 1

X ~ B(10, 0.2) …[Given]
∴ n = 10, p = 0.2
∴ q = 1 – p = 1 – 0.2 = 0.8
The p.m.f. of X is given by
P(X = x) = `""^10"C"_x (0.2)^x (0.8)^(10 - x), x` = 0, 1,...,10
P(X = 1) = `""^10"C"_1 (0.2)^1 (0.8)^(9)`
= 10 (0.2) (0.8)⁹
= 2 (0.8)⁹.