solve it

First off, let's remember that the probability of something NOT happening is 1 - (the probability of that event happening).
Three cases in which the problem gets solved:

1. they both get it at the same time. P = 1/3 * 1/2 = 1/6

2. A gets it, but B does not. P = 1/2 * (1 - 1/3) = 1/2 * 2/3 = 1/3

3. A doesn't get it, but B does. P = (1 - 1/2)*1/3 = 1/2*1/3 = 1/6

Sum of P = 1/6 + 1/6 + 1/3 = 2/6 + 1/3 = 1/3 + 1/3 = 2/3.


Side note: another way of doing this is by noticing that the probability of the problem being solved is 1 - the probability of the event that the problem is not solved by either.

P' = (1 - 1/2)*(1 - 1/3) = 1/2 * 2/3 = 1/3

1 - P' = 1 - 1/3 = 2/3.