The Solution to a Probability Problem

This is a conditional probability problem, which is completed in two steps, and two situations should be considered at the same time:

The probability of dumping boys for the first time is 2/3, and the probability of dumping girls for the next time is 5/14;

The probability of a girl being selected for the first time is 1/3, and the probability of being selected for the next time is 4/ 14.

These two situations add up.

p =(2/3)*(5/ 14)+( 1/3)*(4/ 14)= 1/3