Question

The probability that a certain kind of component will survive a shock test is 3/4. Find the probability that exactly 2 of the next 4 components tested survive test, assuming tests are independent.

Answer 1

Answer:

Therefore the required probability is $=\frac{27}{128}$

Step-by-step explanation:

The probability of success is $\frac{3}{4}$

The number of trial = 4

X= the items survive out of 4

$P(x=r)=^nC_rq^{n-r}p^r$        p =the probability of success and q = the probability failure.

p=$\frac{3}{4}$     and $q=(1-\frac{3}{4})=\frac{1}{4}$

$\therefore P(X=2)=^4C_2(\frac{1}{4} )^2(\frac{3}{4} )^2$

                  $=\frac{4!}{2!2!} (\frac{1}{16} )(\frac{9}{16} )$

                  $=\frac{27}{128}$

Therefore the required probability is $=\frac{27}{128}$