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Question
Solve the following problem :
Let X ∼ B(10,0.2). Find P(X ≥1)
Solution
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) = 1 – P(X < 1) = 1 – P(X = 0)
= `1 - ""^10"C"_0 (0.2)^0 (0.8)^10`
= 1 – (0.8)10.
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