ST 305
Examples: Probability, Odds, Counting
Reiland
Name
Probability, Odds, and Counting
(SOLUTIONS)
1. The following is a breakdown of a sample of 1008 adults that were polled prior to the 2013
Super Bowl concerning their plans for viewing the Super Bowl.
Game
Commercials
Won't Watch
Total
Male
279
81
132
492
Female
200
156
160
516
Total
479
237
292
1008
What is the probability that a viewer is female or is in the “Won’t Watch” category?
P( female)  P(Won ' tWatch)  P( female and Won ' tWatch)
516 292 160


 .512  .290  .159  .643
1008 1008 1008
2. Three fair coins are tossed. What are the odds in favor of getting at least 1 head?
7
P (at least 1 head )  ,so odds in favor of at least 1 head
8
 P (at least 1 head ) to 1  P (at least 1 head )

7
1
to or 7 to 1
8
8
3. After examining a man’s family history, a doctor says that the odds in favor of the man being
bald by age 60 are 9 to 2. What is the probability that the man will be bald by age 60?
P(man will be bald by age 60) 
9
9

9  2 11
4. For each horse race, racetracks display the odds that each horse will lose on a large screen
called a tote board. Below is the tote board for a particular race:
Horse 1 2 to 1
Horse 4 7 to 5
Horse 2 15 to 1
Horse 5 1 to 1
Horse 3 3 to 2
Horse 6 5 to 2
What is the probability that horse 4 will win?
P(horse 4 loses) 
7
7
5
 ,so P(horse 4 wins)  .
7  5 12
12
5. Your laptop computer requires you to designate a 4-digit code using the digits 0 – 9 (you can use
the same digit more than once and order counts) as the password to use your computer. How
many passwords are possible?
104  10,000
6. After graduation you plan on applying to graduate school at 5 universities selected from a list of
20 universities provided by your advisor. To how many different groups of 5 universities can you
apply?
20
C5 
20!
 15,504
5!15!
7. A bank vault containing $1,000,000 has a lock with the numbers 0 through 29 on the dial. One
3-digit sequence of numbers (each number must be different) opens the vault. You want to
break into the vault to get the money but you do not know the 3-digit sequence that opens the
lock. How many 3-digit sequences are possible?
P 
30 3
30!
30!

 24,360
(30  3)! 27!
8. Suppose there are 40 students in class today. How many different simple random samples of 7
students can be selected from the class?
40
C7 
40!
 18, 643,560
7! 33!
9. In a multi-million dollar Powerball lotto game a player must choose 5 different numbers from 1
to 55 (order is not important) and a Powerball number between 1 and 42. To win the jackpot
you must choose all 5 numbers and the Powerball number. A lesser prize of $200,000 is given if
a player chooses the first 5 numbers correctly but chooses the incorrect Powerball number.
What is the probability of winning $200,000?
P(win $200,000)
 P(correctly choose all 5 numbers AND choose incorrect Powerball number)
1
41
41
=


 2.81107  .000000281
42 146,107,962
55 C5