Question

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.

Answer 1

Answer:

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

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

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

$P(A \cap B)$ 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 $P(A) = 0.8, P(B) = 0.6$

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

This means that: $P(A \cup B) = 0.9$

We also have that:

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

So

$0.9 = 0.8+0.6 - P(A \cap B)$

$P(A \cap B) = 0.5$

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

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.5}{0.8} = 0.625$

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