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प्रश्न
The probability of a man hitting a target is 0.25. He shoots 7 times. What is the probability of his hitting at least twice?
उत्तर
Here n = 7
p = 0.25 = `25/100 = 1/4`
And q = `1 - 1/4 = 3/4`
P(X ≥ 2) = 1 – [P(X = 0) + P(X = 1)]
= `1 - [""^7"C"_0 (1/4)^0 (3/4)^7 + ""^7"C"_1 (1/4)^1 (3/4)^6]`
= `1 - [(3/4)^7 + 7/4(3/4)^6]`
= `1 - (3/4)^6 (3/4 + 7/4)`
= `1 - (3/4)^6 (10/4)`
= `1 - 729/4096 xx 10/4`
= `1 - 7290/16384`
= `(16384 - 7290)/16384`
= `9094/16384`
= `4547/8192`
Hence, the required probability is `4547/8192`.
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