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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 A. $37 / 221$ B. $5 / 13$ C. $1 / 13$ D. $2 / 13$

Solution:

D. $2 / 13$

REASON:

A deck of cards is given.

Let X be the total number of aces you’ve gotten.

Therefore Expectation of $\mathrm{X} \mathrm{E}(\mathrm{X})$

$\mathrm{E}(\mathrm{X})=\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{x}_{\mathrm{i}} \mathrm{p}_{\mathrm{i}}$

$=0 \times \frac{1128}{1326}+1 \times \frac{192}{1326}+2 \times \frac{6}{1326}$

$=\frac{204}{1326}$

$\Rightarrow \mathrm{E}(\mathrm{X})=\frac{2}{13}$

As a result, the correct answer is (D).