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

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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) About Me  (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 1-0.65+=+0.35.

The probability that B solves the problem is 0.75, so the probability that B does NOT solve the problem is 1-0.75+=+0.25.

Then the probability that NEITHER A NOR B solves the problem is 0.35%2A0.25+=+.0875

And so the probability that someone solves the problem is 1-.0875+=+0.9125.

And finally the probability that A solves the problem, GIVEN THAT someone solves the problem, is 0.65%2F0.9125+=+0.71233 (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 1-13%2F20+=+7%2F20.

The probability that B solves the problem is 3/4, so the probability that B does NOT solve the problem is 1-3%2F4+=+1%2F4.

Then the probability that NEITHER A NOR B solves the problem is %287%2F20%29%2A%281%2F4%29+=+7%2F80

And so the probability that someone solves the problem is 1-7%2F80+=+73%2F80.

And finally the probability that A solves the problem, GIVEN THAT someone solves the problem, is %2813%2F20%29%2F%2873%2F80%29+=+%2852%2F80%29%2F%2873%2F80%29+=+52%2F73.