A bag contains 4 white marbles and 3 blue marbles. Another bag contains 5 red and 6 blue marbles. If a marble…

Analyze the question

Bag 1: 4 white, 3 blue (7 marbles total). Bag 2: 5 red, 6 blue (11 marbles total). One marble is picked from each bag. We want the probability that both are the same colour.

Concept

Bag 1 has no red marbles and Bag 2 has no white marbles. So the only colour the two bags share is blue. "Same colour" therefore means both marbles are blue.

For independent events: P(A and B) = P(A) × P(B)

Solution

• P(blue from Bag 1) = 3/7
• P(blue from Bag 2) = 6/11

P(both blue) = 3/7 × 6/11 = 18/77

Answer

Tip

Before multiplying anything, list which colours appear in both bags. Here only blue does, so you don't need to consider white or red pairs at all. In "same colour" questions, a colour that is missing from one bag contributes a probability of 0.