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Question
Solve the following problem :
The probability that a bomb will hit the target is 0.8. Find the probability that, out of 5 bombs, exactly 2 will miss the target.
Solution
Let X denote the number of bombs hitting the target.
P(bomb hits the target) = p = 0.8
∴ q = 1 – p = 1 – 0.8 = 0.2
Given, n = 5
∴ X ~ B(5, 0.8)
The p.m.f. of X is given by
P(X = x) `""^5"C"_x (0.8)^x (0.2)^(5 - x), x` = 0, 1,...,5
∴ P(exactly two will miss the target)
= P(exactly three will hit the target)
= P(X = 3)
= `""^5"C"_3 (0.8)^3 (0.2)^(2)`
= `(5!)/(3! xx 2!)(4/5)^3 (1/5)^2`
= `(5 xx 4 xx 3!)/(2 xx 1 xx 3!) xx (4^3/5^5)`
= `10(4^3/5^5)`.
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