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math: expected value/profit?
I am having trouble figuring out the answer.
Q: Andy is gambling. The game costs $2 to play. He draws a card from a deck. If he gets a number card (2-10), he wins nothing. For any face card ( jack, queen or king), he wins $3. For any ace, he wins $5, and he wins an extra $20 if he draws the ace of clubs. What is Andy's expected profit per game?
2 Answers
- Mike GLv 74 years agoFavorite Answer
E(X) = -2+3*(12/52)+5*(3/52)+25*(1/52)
= -2+[36+15+25]/52
= -26/13+19/13
= -7/13
= -$0.54
He will lose on average 54 cents per game
- SqdancefanLv 74 years ago
His expected winnings per game are
.. 12/52*$3 +4/52*$5 +1/52*$20 = $76/53 ≈ $1.46
After subtracting his cost, Andy can expect to lose $0.54 per game.
