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Question
The probability that a certain kind of component will survive a electrical test is `3/4`. Find the probability that exactly 3 of the 5 components tested survive
Solution
Given n = 5
Probability that a component survive in a test = p = `3/4`
∴ q = `1 - "p" = 1 - 3/4 = 1/4`
Let 'x' be the random variable denotes the number of components survived in a test.
Probability of 'x' successes in 'n' trials is
P(X = x) = nCx px qn-x
x = 0, 1, 2, ....., n
Probability that exactly 3 components survive
P(X = 3) = `""^5"C"_3 (3/4)^3 (1/4)^(5 - 3)`
= `10(27/64)(1/16)`
= `270/1024`
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