A bag contains 3 red marbles and 4 blue marbles. a marble is taken at random and replaced. another m

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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