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Binomial Distribution — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsBinomial Distribution3 Marks
Question
The probability that a 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

$\begin{aligned} & p=0.6, q=1-p=1-0.6=0.4 \\ & n=4, r=2 \\ & p(X=r)={ }^n C_r p^r q^{n-r} \\ & p(X=2)={ }^4 C_2(0.6)^2(0.4)^2 \\ & =\frac{4 \times 3}{1 \times 2}(0.36)(0.16) \\ & =0.3456\end{aligned}$

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