Question

Suppose that two cards are drawn at random from a deck of cards. Let X be the number of aces obtained. Then the value of E(X) is

(A) (B) (C) (D)

Answer 1

Let X denote the number of aces obtained. Therefore, X can take any of the values of 0, 1, or 2.

In a deck of 52 cards, 4 cards are aces. Therefore, there are 48 non-ace cards.

∴ P (X = 0) = P (0 ace and 2 non-ace cards) =

P (X = 1) = P (1 ace and 1 non-ace cards) =

P (X = 2) = P (2 ace and 0 non- ace cards) =

Thus, the probability distribution is as follows.

X	0	1	2
P(X)

Then, E(X) =

Therefore, the correct answer is D.