The probability that A will solve a problem is 2/3 and the probability that B will solve the problem is 3/4. What is the probability that? (a) The problem will be solved (b) Neither can solve it.
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2/3rds of the time, A solves it. If so, the chance of B not solving it are 4/4–3/4=1/4, so the total chance of exactly one solving it this way are 2/3*1/4=2/12
3/3-2/3=1/3rd the time A does not solve it. If not, the chance of B solving it are 3/4, so the chance of exactly one solving it this way are 1/3*3/4=3/12
Adding together all the possible cases in which exactly one solves the problem, we have 2/12+3/12=5/12 chance that this occurs.
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