# Expected number of matches

Not what you're looking for? Search our solutions OR ask your own Custom question.

#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.

Â© BrainMass Inc. brainmass.com December 24, 2021, 5:09 pm ad1c9bdddfhttps://brainmass.com/math/probability/expected-number-matches-31317

#### 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;

...

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.

$2.49