Select five cards without replacement from a standard deck of 52, and let X be the number of black cards you draw. Calculate the expected value of the given random variable X.
A) $E ( X ) = 26$
B) $E ( X ) = 1.8$
C) $E ( X ) = 3$
D) $E ( X ) = 2.5$
E) $E ( X ) = 3.2$

Question

Select five cards without replacement from a standard deck of 52, and let X be the number of black cards you draw. Calculate the expected value of the given random variable X.  
A) $E ( X ) = 26$
B) $E ( X ) = 1.8$
C) $E ( X ) = 3$
D) $E ( X ) = 2.5$
E) $E ( X ) = 3.2$

Quizplus · Accepted Answer

The expected value of drawing a black card from a standard deck of 52 cards is calculated by multiplying the probability of drawing a black card by the total number of draws. Since half of the cards (26 out of 52) are black, the probability of drawing a black card in any single draw is 26/52 = 1/2. When drawing five cards, the expected number of black cards is 5 * (1/2) = 2.5.

Select Five Cards Without Replacement from a Standard Deck of 52