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?

Explanation

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.

Here, `{p}=0.2, {q}=0.8`

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`


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