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) = nCrprqn-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 
.