A bag contains 3 red marbles and 4 blue marbles

a marble is taken out of the bag at random and replaced

another marble is taken from the bag

work out the probability that the 2 marbles taken out the bag are the same colour

A bag contains 3 red marbles and 4 blue marbles. a marble is taken at random and replaced. Another marble is taken from the bag. Work out the probability that the two marbles taken from the bag are the same color.

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