Worksheet 10
MAT 1000
Wayne State University
Due: 3/2-3/3
In a standard deck of 52 playing cards, each card has one of four suits (hearts, clubs, diamonds, and
spades) and one of 13 face values (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, ace).
1. In the Texas Hold ‘Em style of poker, each player is dealt 2 cards. From a standard deck of 52
cards, how many possible 2 card hands are there?
(Note that the order of the cards in the hand doesn’t matter: a hand consisting of the 2 of clubs
and the jack of diamonds is the same as a hand consisting of the jack of diamonds and the 2 of
clubs.)
One of the face values is the ace. Since there are four suits, there are four aces in the deck: the ace of
hearts, the ace of clubs, the ace of diamonds, and the ace of spades.
2. How many different 2 card hands are there where both cards are aces?
3. What is the probability of getting a 2 card hand where both cards are aces?
Since there are 13 cards of each suit, 13 cards in the deck are of the suit of hearts.
4. How many different 2 card hands are there where both cards are hearts?
5. What is the probability of getting a 2 card hand where both cards are hearts?
6. I have 30 students in a class. If I want to choose a simple random sample of five of the students,
how many possible different groups of five are there?
(The order does not matter. The group A, B, C, D, E is the same group as E, D, C, B, A, or those
same five people in any other order.)
7. If you are one of the 30 students, how many groups of five are there that include you?
8. If I pick a group of five at random, what’s the probability you are in the group of five that I pick?
TURN OVER
The following table gives data on the distribution of the number of vehicles in American households.
Number of vehicles 0
1
2
3
4
Proportion
0.10 0.34 0.39 0.13 0.04
9. Find the expected value of the probability model.
In a Straight Pick 3 lottery you pick a 3-digit number. A 3-digit number is chosen at random, and you win
$250 if your number is chosen. Here is the probability model for your winnings.
Outcome
Probability
$0
$250
0.999 0.001
10. What is the expected value of this probability model?
Suppose 1,000,000 people play the lottery.
11. What, on average, will each person win, approximately?
12. If tickets cost $1 each, how much profit will the state make (approximately)?
(At $1 per ticket they collect $1,000,000, but they will have to pay out some amount in prizes.
This is the amount you can approximate.)