Question

Exercise 4 Answer following question below

a. You draw a card from a deck. If you get a club you get $5. If you get an Ace you get $10. For all other cards you receive nothing. Let X be the random variable of money won. Create a probability distribution model for this game.

b. You draw a card from a deck. If you get a club you get nothing. If you get red card you get $10. If you get a spade you get $15 and get to select another card (without replacement). If the second is another spade you receive an additional $20. You receive nothing for any non-spade card. Create a probability model for this game.

Answer 1

P(X=$15) = Probability of getting the Ace of clubs = 1/52
P(X=$10) = Probability of getting an Ace other than the Ace of clubs = 12/52 = 4/13
P(X=$5) = Probability of getting a club other than the Ace of clubs = 3/52
P(X=$0) = Probability of getting a card which is neither a club nor an Ace = 36/52 = 9/13

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Let Y be the random variable of money won.

P(Y=$0) = Probability of getting a club = 13/52 = 1/4
P(Y=$10) = Probability of getting a red card = Probability of getting a heart or a diamond = 26/52 = 1/2
P(Y=$15) = Probability of getting a spade and then getting a non-spade card = (13/52)(39/51) = 13/68
P(Y=$35) = Probability of getting a spade and then getting a spade again = (13/52)(12/51) = 1/17