Question

The probability that Billy would pass at least one test is 0.9. The probability that he passes both tests is 0.7. The tests are of equal difficulty (that is, the probability that Billy passes test 1 is the same as the probability that he passes test 2). What is the conditional probability of Billy passing test 2 given the event that he passes test 1?

Answer 1

Answer:

0.875

Step-by-step explanation:

Let the probability that Billy passes test 1 be P(A)

Let the probability that Billy passes test 2 be P(B)

P(A n B) = 0.7

P(A) = P(B)

Let them both be numerically x.

P(A) = P(B) = x

P(A') = P(B') = (1 - x)

Probability that he passes at least one test = 0.9

But (probability that he passes at least 1 test) = 1 - (Probabilty that he fails both tests)

Probability that he fails both tests = 1 - 0.9 = 0.1

P(A' n B')= 0.1

P(U) = P(A) - P(A n B) + P(B) - P(A n B) + P(A n B) + P(A' n B') = 1

x - 0.7 + x - 0.7 + 0.7 + 0.1 = 1

2x = 1 + 0.7 - 0.1 = 1.6

x = 0.8

P(A) = P(B) = 0.8

The conditional probability of Billy passing test 2 given the event that he passes test 1 = P(B|A) = P(A n B)/P(A) = (0.7/0.8)

P(B|A) = 0.875

Hope this helps!!!