Question

Another game involved drawing one card from a standard deck of cards. If you draw a red face card you earn $5. If you draw a black card you are paid $1. If you draw a red ace you will need to draw a second card from the deck (without replacing the first card). If your second card is red you win $80, if it is black you are paid nothing. All other outcomes earn nothing. What is the expected value for this game?

Answer 1

$4.32

Explanation:

The expected value is the sum of each outcome times its probability.

The probability that the first card is red and not an ace is 24/52.

The probability that the first card is black is 26/52.

The probability that the first card is a red ace and the second card is red (without replacing the first card) is (2/52) (25/51).

The probability that the first card is a red ace and the second card is black (without replacing the first card) is (2/52) (26/51).

The expected value is:

X = (24/52) (5) + (26/52) (1) + (2/52) (25/51) (80) + (2/52) (26/51) (0)

X ≈ 4.32

Rounded to the nearest cent, the expected value is $4.32.