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Question
Choose the correct option from the given alternatives:
The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is
Options
`128/256`
`219/256`
`37/256`
`28/256`
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Solution
`28/256`
Explanation:
np = 4, npq = 2
∴ q = `1/2` and p = `1/2`
∴ `"n"(1/2) = 4`
∴ n = 8
∴ P(X = 2) = `"^8C_2 (1/2)^8 = (8 xx 7)/(1 xx 2) xx 1/256 = 28/256`
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