Question

A bag contains three red marbles and two blue marbles. Marcus reaches in and pulls out a marble, replaces it, but then reaches in and pulls out another marble. What is the probability now that they both are blue?

Answer 1

The probability of drawing two blue marbles in succession is 16/49.

Step-by-step explanation:

To find the probability of drawing two blue marbles, we need to calculate the probability of drawing a blue marble on the first draw and then a blue marble on the second draw.

The probability of drawing a blue marble on the first draw is 4 out of 7 (4 blue marbles out of a total of 7 marbles remaining in the bag after the first draw).

Since Marcus replaces the marble after the first draw, the probability of drawing a blue marble on the second draw remains the same, 4 out of 7.

To find the probability of both events happening, we multiply the probabilities together:

P(Blue, then Blue) = P(Blue on first draw) × P(Blue on second draw) = (4/7) × (4/7) = 16/49.