# Expected number of matches

#18. Cards from an ordinary deck of 52 playing cards are turned face up one at a time. If the first card is an ace, or the second a deuce, or the third a three, or ..., or the thirteenth a king, or fourteenth an ace, and so on, we say that a match occurs. Note that we do not require that the (13n + 1)th card be any particular ace for a match to occur but only that it be an ace. Compute the expected number of matches that occur.

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#### Solution Preview

The probability of the first match of an ace is 4/52;

The probability of the second match of a deuce is 4/52;

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The probability of the 13th match of a king is 4/52;

The ...

#### Solution Summary

This shows how to co mpute teh expected number of matches occurring when drawing cards.

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