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Three boxes B1, B2 and B3 contain balls ...

Three boxes `B_1, B_2 and B_3` contain balls with different colours as shown below:

A die is thrown. `B_1` is chosen if either 1 or 2 turns up. `B_2` is chosen if either 3 or 4 turns up. `B_3` is chosen if either 5 or 6 turns up. Having chosen a box in this way, a ball is chosen at random from this box. If the ball drawn is found to be red, find the probability that it is drawn from box `B_2`.

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