Multiple choice

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 $E\left(X\right)$ is

  1. $\displaystyle\frac{37}{221}$
  2. $\displaystyle\frac{5}{13}$
  3. $\displaystyle\frac{1}{13}$
  4. $\displaystyle\frac{2}{13}$
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D Correct answer
Explanation

Drawing 2 cards from 52. Expected number of aces E(X) = n * p, where n = 2 and p = 4/52 = 1/13. E(X) = 2 * (1/13) = 2/13.

AI explanation

The random variable X follows a hypergeometric distribution, and its expected value can be calculated using the formula E(X) = n times (K/N). Here, n is 2 cards drawn, K is 4 aces in the deck, and N is the 52 total cards. Substituting these values gives E(X) = 2 times (4/52), which equals 2/13.

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