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We have three balls, let us call them a, b, c. We have three bins, let us call them A, B, C. We randomly place

We have three balls, let us call them a, b, c. We have three bins, let us call them A, B, C. We randomly place each ball in a different bin. All 3! possible assignments are equally likely.

(a) Compute the probability that ball c is placed in bin C.

(b) Compute the probability that ball c is placed in bin C given that ball a is not placed in bin A.

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