A box contains 24 marbles. The probability that a randomly drawn marble is green is 2/3. How many marbles in the box are blue?

Introduction / Context:This is a direct conversion between probability and counts. If a colour has probability 2/3 in a finite uniform selection, then 2/3 of the items must be of that colour.

Given Data / Assumptions:

• Total marbles = 24.
• P(green) = 2/3 → green count = (2/3)*24.
• All non-green marbles are blue.

Concept / Approach:Compute the number of green marbles and subtract from the total to get the number of blue marbles.

Step-by-Step Solution:Green marbles = (2/3)*24 = 16.Blue marbles = 24 − 16 = 8.

Verification / Alternative check:Check probability: 16/24 = 2/3 is consistent with the given probability.

Why Other Options Are Wrong:12 and 13 are incorrect residual counts; 16 is the green count, not blue.

Common Pitfalls:Applying the 2/3 to the wrong colour or forgetting that only two colours are present.

Final Answer:8