Question

A bag contains 3 red marbles and 4 blue marbles.

A marble is taken at random from the bag and replaced.
Another marble is taken from the bag.

Work out the probability that the 2 marbles taken from the bag are the same colour.

Give your answer as a fraction.

Answer 1

Total number of marbles in the bag is 3 + 4 = 7.

The problem asks for the probability of (RR) or (BB).

It's worthy to note we are replacing the balls after each draw, which means we always have 7 to draw from

Since each draw is independent, we take the product of each event for the total event probability.

P(RR) = 3/7 * 3/7 = 9/49

P(BB) = 4/7 * 4/7 = 16/49

We want to know P(RR) + P(BB)

P(RR) + P(BB) = 9/49 + 16/49 = 25/49