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.
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')"
"+({1\\over 8}*{5 \\over 6} * {2 \\over 3})"
"\\therefore P(machine \\space running \\space continuously) = {43 \\over 48}"
Probability of machine failing
"=1 - {43 \\over 48}"
"={5 \\over 48}"
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