Sorry guys I didnot review this post earlier.

We add them because these two probabilities represent two scenarios, either of which will satisfy the condition.

The first one is that Mary will pick a white ball \(\left(P=\frac{3}{8}\right)\) and then John will pick a blue one with the probability of \(\frac{5}{7}\) (note that Mary keeps her white ball and John picks his from the 7 left, not 8).

The second scenario is that Mary picks a blue ball \(\left(P=\frac{5}{8}\right)\) and John picks a blue ball with a probability of \(\frac{4}{7}\).

We have to add the probabilities of both scenarios because either of them is good for us:

\(\frac{3}{8}*\frac{5}{7} + \frac{5}{8}*\frac{4}{7} = \frac{35}{56} = \frac{5}{8}\)

Hope this helps.

Economist wrote:

Hi Gmat tiger,

why do we add these two probabilites and not multiply?

Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html

Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT