Question

Problem 10 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

We begin first with listing the outcomes and payoffs

Card	Payout
Club	$0
Red	$10
Spade and spade	15 + 20 = $35
Spade and non-spade	15 + 0 = $15

When a spade is drawn there is a chance to draw another card. Hence, we join the chances of drawing the 2nd card along with 1st card.

Probability

Now we join the probability

Card	Probability
1. Club There are 13 clubs in a deck. Hence, the probability of getting a club out of 52	= 0.25
2. Red There are 26 reds (hearts and diamonds) in a deck. Hence, the probability to get a red out of 52	= 0.5
3. Spade and spade	= 0.0588
4. Spade and non-spade	= 0.1912

For 3 & 4

The events of drawing 1st card and 2nd card are independent. So we multiply the probability of the cards.

There are 13 spades so probability of 1st card being spade =

Since the second card drawn is without replacement. Now in the deck only 51 cards will be left with 12 spades and 39 non-spade cards.

If 2nd card is also spade then the possibility

If 2nd card is a non - spade then the possibility

For a probability model all the outcomes along with their probability have to be listed. The sum of probabilities should be equal to 1.

Card	Payout	Probability
Club	$0	0.25
Red	$10	0.5
Spade and spade	$35	0.0588
Spade and non-spade	$15	0.1912
Total		1