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प्रश्न
Let X ~ B(10, 0.2). Find P(X ≤ 8).
उत्तर
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`
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