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?

Let p be the probability of the tube to function for more than 500 hours.

This probability is given as 0.2.

⇒ p = 0.2

If p is the probability of the tube to function for more than 500 hours, then q is the probability of the tube to not function for more than 500 hours.

⇒ p + q = 1

⇒ q = 1 – p

Let X denote a random variable that represents the number of the tube that can function for more than 500 hours out of the total 4 tubes.

And let n denote the total number of tube taken in the sample, that is, 4.

Then binomial distribution for r tube to function more than 500 hours out of 4 tubes is given by,

P (X = r) = ^{n}C_{r}p^{r}q^{n-r}

Putting n = 4, and above, we get

We need to find the probability that exactly 3 tubes will function for more than 500 hours.

So, put r = 3. We get

Thus, the probability that exactly 3 tubes will function for more than 500 hours is .

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