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There are three bags B(1), B(2) and B(3)...

There are three bags `B_(1), B_(2)` and `B_(3)`. The bag `B_(1)` contains 4 red and 4 black balls, `B_(2)` contains 3 red and 4 black balls, `B_(3)` contains 4 red and 3 black balls. Bags `B_(1), B_(2)` and `B_(3)` have probabilities `(1)/(6), (1)/(3)` and `(1)/(2)` respectively of being chosen. A bag is selected at random and a ball is chosen at random from the bag. Then probability of getting a red ball is?

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