Maharashtra State BoardHSC Arts 12th Board Exam
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Let X ~ B(10, 0.2). Find P(X ≥ 1). - Mathematics and Statistics

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Sum

Let X ~ B(10, 0.2). Find P(X ≥ 1).

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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) = 1 - P(X < 1)

= 1 - P(X = 0)

= 1 - `"^10C_0 (0.2)^0 (0.8)^(10 - 0)`

`= 1 - 1 xx 1 xx (0.8)^10`

`= 1 - (0.8)^10`

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 1.2 | Page 253
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