An urn contains 2 red, 3 green, and 2 blue balls. If 2 balls are drawn at random, find the probability that neither ball is blue.

Question: An urn contains 2 red, 3 green, and 2 blue balls. If 2 balls are drawn at random, find the probability that neither ball is blue.

Solution:
Total number of balls = (2 + 3 + 2)
= 7

Let, E be the event of drawing 2 non-blue balls.

Then,
n (E) = ⁵C₂
= (5 × 4)/(2×1)
= 10

And, n (S) = ⁷C₂
= (7 × 6)/(2 × 1)
= 21

∴ P(E) = n(E)/n(S) = 10/21