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?

Answer 1

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.

$$\begin{gathered} \mathrm{Here}\mathit{,}\mathit{}p=0.2,q=0.8 \\ \mathrm{Hence},\mathrm{the}\mathrm{distribution}\mathrm{is}\mathrm{given}\mathrm{by} \\ P(X=r)={}^{4}C_r(0.2{)}^r(0.8{)}^{4-r},r=0,1,2,3,4 \\ \mathrm{Therefore},\mathrm{required}\mathrm{probability}=P(X=3) \\ =4(0.2{)}^3(0.8) \\ =0.0256 \end{gathered}$$