From a pack of 5 green balls and 4 red balls, 2 balls are drawn at random. What is the probability that both the balls are of the same colour ?
5/9
4/9
2/9
None of the above
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CISF-AC-EXE – 2022
We are drawing 2 balls at random.
The total number of ways to choose 2 balls out of 9 is given by the combination formula C(n, k) = n! / (k! * (n-k)!):
Total outcomes = C(9, 2) = 9! / (2! * 7!) = (9 × 8) / (2 × 1) = 36.
We want the probability that both balls are of the same colour. This can happen in two mutually exclusive ways:
Case 1: Both balls are green.
Number of ways to choose 2 green balls out of 5 = C(5, 2) = 5! / (2! * 3!) = (5 × 4) / (2 × 1) = 10.
Case 2: Both balls are red.
Number of ways to choose 2 red balls out of 4 = C(4, 2) = 4! / (2! * 2!) = (4 × 3) / (2 × 1) = 6.
The number of favourable outcomes (both balls of the same colour) = Number of ways (both green) + Number of ways (both red) = 10 + 6 = 16.
The probability that both balls are of the same colour is (Favourable outcomes) / (Total outcomes) = 16 / 36.
Simplifying the fraction, 16/36 = (4 × 4) / (9 × 4) = 4/9.