Question

Solve the following problem :

Let X ∼ B(10,0.2). Find P(X ≤ 8).

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 ≤ 8) = 1 – P (X > 8) = 1 – P(X = 9 or X = 10)
= 1 – [P(X = 9) + P(X = 10)]
= `1 - [""^10"C"_9 (0.2)^9 (0.8) + ""^10"C"_10 (0.2)^10 (.8)^0]`
= 1 – (0.2)⁹ [10 x 0.8 + 0.2]
= 1 – (8.2) (0.2)⁹.