23. There are n cards in a box numbered 1 through n. We draw cards successively and...

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23. There are n cards in a box numbered 1 through n. We draw cards successively and at random with replacement. If the ith draw is the card numbered i, we say that a match has occurred.

(a) What is the probability of at least one match in n trials?

(b) What happens if n increases without bound?

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