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# Solve the following problem : Let X ∼ B(10,0.2). Find P(X ≤ 8). - Mathematics and Statistics

Sum

Solve the following problem :

Let X ∼ B(10,0.2). Find P(X ≤ 8).

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#### 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 ≤ 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.

Concept: Mean of Binomial Distribution (P.M.F.)
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Probability Distributions
Part II | Q 1.01 | Page 156
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