Suppose that I deal you two cards to begin a hand of Blackjack. Let X record the total number of face cards that you are dealt. What is the sample space for X?

Question

a. S= {face card, no face card}
b. S= {face card + face card, face card + no face card, no face card + face card, no face card + no face card}
c. S= {1,2}
d. S= {0,1,2}

Answer 1

d. S = {0, 1, 2}

Answer 2

why is it not option b?

Answer 3

Option b is not the correct answer because it lists four possible outcomes, whereas only three outcomes are possible when dealing only two cards: 0 face cards, 1 face card, or 2 face cards.

In option b, "face card + face card" and "no face card + no face card" suggest that there are possibilities for two face cards or two non-face cards, which is not possible when dealing only two cards from a standard deck of playing cards.