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Problem 86: Human error is given as the reason for 75% of all accidents in a plant. Use the formula for the binomial distribution to find the probability that human error will be given as the reaosn for two of the next four accidents.

Problem 86: Human error is given as the reason for 75% of all accidents in a plant. Use the formula for the binomial distribution to find the probability that human error will be given as the reaosn for two of the next four accidents.

Solution:


a. Given that $x=2, n=4,$ and $p=0.75$
$b(x;n,p)=\left(\begin{array}{c}n\\ x\end{array}\right){p}^{x}(1-p)^{n-x}$
$b(2;4,0.75) = \left(\begin{array}{c}4\\ 2\end{array}\right){0.75}^{2}(1-0.75)^{4-2}$
$ = ^{4}C_{2}{0.75}^{2}(0.25)^{2}= 6({0.75}^{2})(0.25^{2}) = 0.2109.$

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