It costs $5 to play a game where you draw one card from aregular 52 card deck. I

Question

It costs $5 to play a game where you draw one card from aregular 52 card deck. If you draw a black card you win nothing. Ifyou get a diamond you win $10. If you get a heart you win $20 plusan extra $50 for the ace or king of hearts. Create a probabilitymodel for the net amount you win or lose the game. It costs $5 to play a game where you draw one card from aregular 52 card deck. If you draw a black card you win nothing. Ifyou get a diamond you win $10. If you get a heart you win $20 plusan extra $50 for the ace or king of hearts. Create a probabilitymodel for the net amount you win or lose the game.

Explanation / Answer

Let X be the net amount of win/loss Then, P(X=-5) = 26/52 = 1/2 (drawing a black card) P(X=5) = 13/52 = 1/4 (drawing a diamond) P(X = 65) = 2/52 = 1/26 (drawing ace or king of hearts) P(X = 15) = 11/52 (drawing a heart, but not ace or king ofheart) Note that the sum of probabilities equals to 1:1/2+1/4+1/26+11/52 = 1

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