Mark A machine has two parts labeled A and B. The probability that part A works for one year is 0.8 and the probability that part B works for one year is 0.6. The probability that at least one part works for one year is 0.9. Calculate the probability that part B works for one year, given that part A works for one year.

0.625 = 62.5% probability that part B works for one year, given that part A works for one year.

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

In which

P(B|A) is the probability of event B happening, given that A happened.

is the probability of both A and B happening.

P(A) is the probability of A happening.

The probability that part A works for one year is 0.8 and the probability that part B works for one year is 0.6.

This means that

The probability that at least one part works for one year is 0.9.

This means that:

We also have that:

So

Calculate the probability that part B works for one year, given that part A works for one year.

0.625 = 62.5% probability that part B works for one year, given that part A works for one year.

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