There are two ways the man can select two balls of the same color:
Scenario 1: Both balls are black
The probability of selecting one black ball is
. After taking out one black ball, there are only 4 black balls left and 8 total balls. So, the probability of selecting another black ball is
.
The probability of scenario 1 is then:
×=.
Scenario 2: Both balls are white
The probability of selecting one white ball is
. After taking out one white ball, there are only 3 white balls left and 8 total balls. So, the probability of selecting another white ball is
.
The probability of scenario 2 is then:
×=.
Total Probability
To get the probability of selecting two balls of the same color, we add the probabilities of the two scenarios:
+==