UPSC NDA I 2024 Mathematics Paper

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 ‌

5

9

. 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 ‌

4

8

.
The probability of scenario 1 is then: ‌

5

9

×‌

4

8

=‌

5

18

.
Scenario 2: Both balls are white
The probability of selecting one white ball is ‌

4

9

. 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 ‌

3

8

.
The probability of scenario 2 is then: ‌

4

9

×‌

3

8

=‌

1

6

.
Total Probability
To get the probability of selecting two balls of the same color, we add the probabilities of the two scenarios:
‌

5

18

+‌

1

6

=‌

8

18

=‌

4

9