help... math problem?

Question

Tom and Alice work independently in an attempt to solve a certain problem, i.e. whether one of them solves it does not affect the chances that the other will solve it. The probability that Tom solves it is 0.15 and the probability that Alice solves it is 0.5.

What is the probability that the problem will be solved?


If the problem is solved, what is the probability that Tom solves it?

Answer 1

A. The probability that it will BE solved is 1 - prob that it WON'T be solved. That is 1.00 - (1.00 - .015 [Tom doesn't]) * (1.00 - 0.50 [Alice doesn't]).

= 1.00 - (.85) * (.50). = 1.000 - .425 = .575

B. If Tom solves it then it is 150 / 575 = 6/23