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?
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}
d. S = {0, 1, 2}
why is it not option b?
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.
To determine the sample space for the number of face cards you are dealt in a hand of Blackjack, we can assess all the possible outcomes.
In a standard deck of cards, there are 12 face cards (4 Kings, 4 Queens, and 4 Jacks). Other cards in the deck are not considered face cards.
When you are dealt two cards, there are three possible outcomes for the number of face cards you can get:
1. You can get no face cards,
2. You can get one face card,
3. You can get two face cards.
So, the correct answer is d. S= {0,1,2}