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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).
A random variable X has the following probability distribution:
X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
P(X) | 0 | k | 2k | 2k | 3k | K2 | 2 K2 | 7 K2 + k |
Determine
(i) k (ii) P(X < 3)
(iii) P(X > 6) (iv) P(0 < X < 3)