Question

Let X ~ B(10, 0.2). Find P(X ≤ 8).

Answer 1

X ~ B(10, 0.2)

∴ 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) = `"^nC_x  p^x  q^(n - x)`

∴ P(X = x) = `"^10C_x  (0.2)^x  (0.8)^(10 - x)`, x = 0, 1, 2, 3,....,10

P(X ≤ 8) = 1 - P(X > 8)

= 1 - [P(X = 9) + P(X = 10)]

`= 1 - [""^10C_9 (0.2)^9 (0.8)^(10 - 9) + "^10C_10 (0.2)^10 (0.8)^(10-10)]`

`= 1 - [10 (0.2)^9 (0.8)^1 + 1(0.2)^10 (0.8)^0]`

`= 1 - (0.2)^9 [10(0.8) + (0.2)]`

`= 1 - (0.2)^9 [8 + 0.2]`

`= 1 - (8.2)(0.2)^9`