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Cards from an ordinary deck of 52 playing cards are turned face up one at a time. If the 1st card is an ace, or the 2nd a deuce, or the 3rd a three, or ..., or the 13th a king, or the 14 an ace, and so on, we say that a match occurs. Note that we do not require that the (13n + 1) card be any particular age for a match to occur but only that it be an ace. Compute the expected number of matches that occur.

1 Answer

3 votes

Answer:

4

Explanation:

Given:

Number of cards = 52

Let probability of match, p =
(1)/(13)

Let X follow a binomial distribution.

Thus,

X ~ B
[52, (1)/(13)]

To compute the expected number of matches that occur would be:


E(X) = np= 52[(1)/(13)]

Solving further, we have:


52 * (1)/(13) = 4

Therefore, the expected number of matches that occur is 4.

User Tiago Rangel
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