Let X ~ B(10, 0.2). Find P(X = 1). - Mathematics and Statistics

Sum

Let X ~ B(10, 0.2). Find P(X = 1).

Solution

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 = 1) = "^10C_1  (0.2)^1  (0.8)^(10 - 1)

= 10 (0.2)^1 (0.8)^9 = 2 (0.8)^9

Concept: Binomial Distribution
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 8 Binomial Distribution
Miscellaneous exercise 8 | Q 1.1 | Page 253