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Suppose there are two full bowls of cookies. Bowl #1 has 11 chocolate chip and 22...

Suppose there are two full bowls of cookies. Bowl #1 has 11 chocolate chip and 22 plain cookies, while bowl #2 has 23 of each. Our friend Fred picks a bowl at random, and then picks a cookie at random. The cookie turns out to be a plain one. What is the probability that Fred picked Bowl #1?

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