The probability that certain kind of component will survive a che… - Vidyadip

Question

The probability that certain kind of component will survive a check test is $0.6.$ Find the probability that exactly $2$ of the next $4$ tested components survive

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Answer

Let $X$ denote the number of tested components survive.
$P($ component survive the check test $)=p=0.6$[Given]
$ \therefore q=1-p$
$=1-0.6$
$=0.4 $
Given, $n =4$
$\therefore X \sim B (4,0.6)$
The p.m.f. of $X$ is given by
$P ( X = x )={ }^4 C _x(0.6)^x(0.4)^{4-x}, x=0,1, \ldots, 4$
$\therefore P$ (exactly 2 components tested survive)
$ =P(X=2)$
$={ }^4 C_2(0.6)^2(0.4)^2$
$=6(0.36)(0.16)$
$=0.3456 $

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