Answer to Question #166679 in Statistics and Probability for Bikram Chaudhary

Question #166679

At the begining of each day, the three motors required for the operation of a machine are checked and tested. These motors then have probabilities of 7/8, 5/6 and 2/3 of continuously operating through out a working day. If the production can be maintained as long as two of three motors are operating, calculate the probability of the machine not failing on a particular day. Calculate also the probability of the machine failing for a particular day.


1
Expert's answer
2021-02-25T05:08:48-0500

Solution

Let :

Motor not failing be denoted by F'

Motor failing be denoted by F

P(machine not failing)= P(at least 2 motors don't fail)

"=P(f'f'f') +P(f'f'f) +P(f'ff') +P (ff'f')"


"=({7\\over 8}*{5 \\over 6} * {2 \\over 3})+({7\\over 8}*{5 \\over 6} * {1 \\over 3})+({7\\over 8}*{1 \\over 6} * {2 \\over 3})"

"+({1\\over 8}*{5 \\over 6} * {2 \\over 3})"


"={35 \\over 72}+{35 \\over 144} +{7 \\over 72}+{5 \\over 72}={43 \\over 48}"

"\\therefore P(machine \\space running \\space continuously) = {43 \\over 48}"



Probability of machine failing


"P(machine \\space fail) =1-P(machine \\space not \\space fail)"

"=1 - {43 \\over 48}"

"={5 \\over 48}"


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