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There are two bags of balls. There are 60 white balls and 40 black balls in...

There are two bags of balls. There are 60 white balls and 40 black balls in the first bag. The second bag contains 70 white balls and 30 black balls. Randomly choose one bag and then randomly get one ball from that bag. If you get a black ball, throw a coin and if the coin lands head, report black otherwise report white. If you get a white ball, report white ball. If we get a report of a black ball, what is the probability that the ball is obtained from the first bag?

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