A jar contains 2 red, 3 green and 5 blue marbles. One marble is drawn at random and not replaced. What is the probability that the second marble drawn is green given that the first marble drawn was blue?

Step-by-step solution

1. Total marbles initially = 2+3+5 = 10.
2. Since the first marble is known to be blue, one blue marble is removed, leaving 5-1 = 4 blue marbles.
3. Remaining marbles = 2 red + 3 green + 4 blue = 9.
4. Number of favourable green marbles = 3.
5. Probability = favourable / total = $\frac{3}{9}$.
6. Simplify if desired: $\frac{3}{9}=\frac{1}{3}$.

Concept tested: Conditional probability

Published 5 September 2026 · How this solution was prepared and checked