Question

It is known that machines A, B, C work independently. And their working probabilities are 0.7, 0.8, 0.9 in a day respectively. Find the probability that at most one machine does not work in a day.
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Answer 1

Answer:

Required probability =

P(A) P(B) P(C) + P(A)' P(B) P(C) + P(A) P(B)' P(C) + P(A) P(B) P(C)' =

$(0.7 \times 0.8 \times 0.9 )+ (0.3 \times 0.8 \times 0.9) +( 0.7 \times 0.2 \times 0.9) + (0.7 \times 0.8 \times 0.1) = 0.504 + 0.216 + 0.126 + 0.056 = 0.902$