# Let X ~ B(10, 0.2). Find P(X ≤ 8). - Mathematics and Statistics

Sum

Let X ~ B(10, 0.2). Find P(X ≤ 8).

#### 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 ≤ 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

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 1.3 | Page 253