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Question
Suppose that a radio tube inserted into a certain type of set has probability 0.2 of functioning more than 500 hours. If we test 4 tubes at random what is the probability that exactly three of these tubes function for more than 500 hours?
Solution
Let X denote the number of tubes that function for more than 500 hours.
Then, X follows a binomial distribution with n =4.
Let p be the probability that the tubes function more than 500 hours.
\[\text{ Here} , p = 0 . 2, q = 0 . 8\]
\[\text{ Hence, the distribution is given by} \]
\[P(X = r) = ^{4}{}{C}_r (0 . 2 )^r (0 . 8 )^{4 - r} , r = 0, 1, 2, 3, 4\]
\[\text{ Therefore, required probability } = P(X = 3) \]
\[ = 4(0 . 2 )^3 (0 . 8)\]
\[ = 0 . 0256\]
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