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Suppose that two cards are drawn at ran...

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)`

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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) =`4^C 0×^48 C^2/52^C^2 = 1128/1326`
P (X = 1) = P (1 ace and 1 non-ace cards) =`4^C^1×^48C^1/52^C^2 = 192/1326`
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