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

Given: A deck of cards.

X be the number of aces obtained.

Hence, X can take value of 0, 1 or 2.

As we know, in a deck of 52 cards, 4 cards are aces. Therefore 48 cards are 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)

Hence, the required probability distribution is,

X | 0 | 1 | 2 |

P(X) |

Therefore Expectation of X E(X):

Hence, the correct answer is (D).

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