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

Answer:

4

Step-by-step explanation:

Given:

Number of cards = 52

Let probability of match, p = $\frac{1}{13}$

Let X follow a binomial distribution.

Thus,

X ~ B $[52, \frac{1}{13}]$

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

$E(X) = np= 52[\frac{1}{13}]$

Solving further, we have:

$52 * \frac{1}{13} = 4$

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