Expected value question (2)

Question

You draw one card from a standard 52 card deck. You win $20 if you pull a face card (king, queen, or jack), $30 if you pull a Number 10 Card, and nothing if you pull any other card. It costs $5 to play the game.

What is the expected value? Make sure to type your answer as $0.00 (with two decimals) If the expected value is negative, type your answer as -$0.00 (with two decimals).

Answer 1

Pr(Face card) = 3/13

Pr(10) = 1/13

$20(3/13) + $30(1/13) +0(9/13)-$5 = 90/13-5 =$1.92 expected value

Play it 13 times you expect to win 3($20)+ $30 - 13($5) = 90-65 = $25

each time you played, your expected winnings were 25/13 = $1.92