Question

Billy takes two tests in his probability and statistics class. 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

0.875 is the required probability.

Explanation:

We are given the following in the question:

Probability Billy would pass atleast one test = 0.9

`P(A\cup B) = 0.9`

Probability Billy would pass both test = 0.7

`P(A\cap B) = 0.7`

The two test are equally difficult.

`P(A) = P(B)`

For independent events we can write that

`P(A\cup B) = P(A) + P(B) -P(A\cap B)\\0.9 = 2P(A) - 0.7\\2P(A) = 1.6\\P(A) = P(B)=0.8`

We have to find the conditional probability that Billy passing test 2 given the event that he passes test 1.

`P(B|A) = (P(B\cap A))/(P(A)) = (0.7)/(0.8) = 0.875`

0.875 is the conditional probability of Billy passing test 2 given the event that he passes test 1