SOLUTION: Please help... I am confused. A and B are trying to solve a problem. A has a chance of 65%, B has a chance of 75% solving the problem. What is the probability of A solves the prob

Question 1096149: Please help... I am confused.
A and B are trying to solve a problem. A has a chance of 65%, B has a chance of 75% solving the problem. What is the probability of A solves the problem given that someone solved the problem.
Thank you.
Answer by greenestamps(13334) (Show Source): You can put this solution on YOUR website!

The probability that A solves the problem is 0.65, so the probability that A does NOT solve the problem is .

The probability that B solves the problem is 0.75, so the probability that B does NOT solve the problem is .

Then the probability that NEITHER A NOR B solves the problem is

And so the probability that someone solves the problem is .

And finally the probability that A solves the problem, GIVEN THAT someone solves the problem, is (to 5 decimal places).

If you want an exact answer, use fractions instead of decimals:

The probability that A solves the problem is 13/20, so the probability that A does NOT solve the problem is .

The probability that B solves the problem is 3/4, so the probability that B does NOT solve the problem is .

Then the probability that NEITHER A NOR B solves the problem is

And so the probability that someone solves the problem is .

And finally the probability that A solves the problem, GIVEN THAT someone solves the problem, is .

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