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Problem 87: If the probability is 0.4 that steam will condese in a thin walled aluminum tube at 10atm pressure, use the formula for the binmial disrtibution to find the probability that, under the stated conditions, steam will condense in 4 of 12 such tubes.

Problem 87: If the probability is 0.4 that steam will condese in a thin walled aluminum tube at 10atm pressure, use the formula for the binmial disrtibution to find the probability that, under the stated conditions, steam will condense in 4 of 12 such tubes.

Solution:


a. Given that $x=4, n=12,$ and $p=0.4$
$b(x;n,p)=\left(\begin{array}{c}n\\ x\end{array}\right){p}^{x}(1-p)^{n-x}$
$b(4;12,0.4) = \left(\begin{array}{c}12\\ 4\end{array}\right){0.4}^{4}(1-0.4)^{12-4}$
$ = ^{12}C_{4}{0.4}^{4}(0.6)^{8}= 495({0.4}^{4})(0.6^{8}) = 0.212841.$

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