We have three similar bags B1, B2 and B3 containing 4 balls each. B1 contains 2 red and 2 blue balls, B2 contains 3 red and 1 blue balls and B3 contains 1 red and 3 blue balls

We have three similar bags B1, B2 and B3 containing 4 balls each. B1 contains 2 red and 2 blue balls, B2 contains 3 red and 1 blue balls and B3 contains 1 red and 3 blue balls. One bag is selected at random and a ball is selected at random from that bag.
What is the probability that the ball is red?

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