Consider the following game. You select a card at random from a well shuffled standard 52-card deck.

Question

If the card selected is red and it is a face card (face is Jack, Queen or King) then you win $10. Otherwise you have to pick again. If the second card is red and it is a face card, you win $5. If not, you have to give $3 (so you “win” minus 3 dollars).

a) Create a probability model for this game

Answer 1

You can diagram this with a decision tree:

Draw first card

_________________|________________

| |

Red Face Card (6/52) Other (46/52)

$10 __________|___________

| |

Red Face Card (46/51) Other(5/51)

$5 –$3

Now it's easier to see that the probability of getting $10 is 6/52, the probability of getting $5 is 46*46 / (52*51), and the probability of getting –$3 is 46*5 / (52*51)