Billy takes two tests in his probability and statistics class.

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?

 

 

The answer is apparently 7/8, but I have no idea how???

Answer 1

Let p = probability of passing a test.  Then P(failed both) = (1 -  p)² since the passing of either test is said to be the same.

 

Solving the equation (1 - p)² = 0.1 gives p = about 0.68377 

 

but then it is alleged that the probability of passing both tests is 0.7 and that should be p².  Since p squared is 0.46754, you see that this data is contradictory.

 

Therefore, I believe this problem to be faulty.