A box contains 2 red, 3 blue, and 5 green marbles. Two marbles are drawn successively with replacement. Find the probability that both drawn marbles are green.

Step-by-step solution

1. Calculate the total number of marbles: $2+3+5=10$.
2. Find the probability of drawing a green marble in one draw: $\frac{5}{10}=\frac{1}{2}$.
3. Because the draws are with replacement, the probability for each draw remains $\frac{1}{2}$.
4. Multiply the probabilities of the two independent draws: $\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}$.

Concept tested: Probability with replacement

Published 28 September 2026 · How this solution was prepared and checked

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