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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) `37/221`
(B) 5/13
(C) 1/13
(D) 2/13
Solution
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
'
Thus, the probability distribution is as follows.
| X | 0 | 1 | 2 |
| P(X) | 1128/1326 | 192/1326 | 6/1326 |
Therefore, the correct answer is D.
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