Question

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.

Answer 1

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.