Question

in a card game (using a standard DECK of cards), you pay $5 to draw a single card. If you draw an Ace, you win $20. If you draw a face card, you win $10. If you draw a 2, you win $5.

a) Fill in the probability distribution below:
X 5 10 20
P(X)
b) What is the expected value?
c) Is the game fair? Why or why not?

Answer 1

What's the probability of drawing an ace out of a standard deck? i.e. of the 52 possible cards, how many are aces?

Answer 2

4 @sithsandgiggles

Answer 3

Right, so the probability of drawing an ace is \(\dfrac{4}{52}\).

How many face cards/2s are there? The probability of drawing a face card is \(\dfrac{\text{number of face cards}}{\text{number of cards in deck}}\), and similarly, the probability of drawing a 2 is \(\dfrac{\text{numbers of 2s}}{\text{number of cards in deck}}\).