Section PC.2 Practice Problems
Write answers as whole numbers or simplified fractions unless otherwise noted.
1. A test was given to a group of students. The grades and gender are summarized below.
| A | B | C | Total | |
| Male | 8 | 18 | 13 | 39 |
| Female | 10 | 4 | 12 | 26 |
| Total | 18 | 22 | 25 | 65 |
a. Find the probability that a student chosen at random was female.
b. Find the probability that a student chosen at random did NOT earn a C?
2. The table below shows the number of credit cards owned by a group of individuals.
| Zero | One | Two or More | Total | |
| Male | 9 | 5 | 19 | 33 |
| Female | 18 | 10 | 20 | 48 |
| Total | 27 | 15 | 39 | 81 |
a. Find the probability that a person chosen at random had no credit cards.
b. Find the probability that a person chosen at random has at least one credit card?
3. If you pick one card at random from a standard deck of 52 cards, what is the probability it is not the Ace of Spades?
4. If you pick one card at random from a standard deck of 52 cards, what is the probability it is not a heart?
5. If you pick one card at random from a standard deck of 52 cards, what is the probability it is not a 6?
6. If the probability of a given event is [latex]\frac{24}{61}[/latex], what is the probability of the event not happening?
7. If the probability of a given event not happening is [latex]\frac{38}{45}[/latex], what is the probability of the event happening?
8. Find the probability that the spinner does not land in a blue region. Assume that it is equally probable that the pointer will land on any one of the ten colored regions. If the pointer lands on a borderline, spin again.
9. The table below shows data collected in a college classroom. Find the probability that a student chosen at random does not drive a car.
| Means of Transportation | Number of Students |
| Bike | 7 |
| Car | 2 |
| Bus | 5 |
| Walk | 6 |
10. A single die is rolled twice. The 36 equally likely outcomes are shown as follows. Find the probability of not rolling a sum of 5.
| 1 , 1 | 1 , 2 | 1 , 3 | 1 , 4 | 1 , 5 | 1 , 6 |
| 2 , 1 | 2 , 2 | 2 , 3 | 2 , 4 | 2 , 5 | 2 , 6 |
| 3 , 1 | 3 , 2 | 3 , 3 | 3 , 4 | 3 , 5 | 3 , 6 |
| 4 , 1 | 4 , 2 | 4 , 3 | 4 , 4 | 4 , 5 | 4 , 6 |
| 5 , 1 | 5 , 2 | 5 , 3 | 5 , 4 | 5 , 5 | 5 , 6 |
| 6 , 1 | 6 , 2 | 6 , 3 | 6 , 4 | 6 , 5 | 6 , 6 |
11. An American roulette wheel has 38 slots: 18 red, 18 black, and 2 green.
a. What is the probability of the ball landing in a green slot?
b. What is the probability of the ball not landing in a green slot?
c. What are the odds for the ball landing in a green slot?
d. What are the odds against the ball landing in a green slot?
12. The weatherman says that there is a 68% chance of rain today.
a. What is the probability, as a simplified fraction, that it will not rain today?
b. What are the odds that it will rain today?
c. What are the odds that it will not rain today?
13. If the probability of a given event is [latex]\frac{51}{82}[/latex], what are the odds for the event happening?
14. If the probability of a given event is [latex]\frac{46}{78}[/latex], what are the odds against the event happening?
15. The probability of not getting a speeding ticket is 16%, what are the odds of getting a ticket?
16. Find the odds for rolling a die and getting a 1.
17. Find the odds against rolling a die and getting an even number.
18. Find the odds for rolling a die and not getting a 6.
19. If you pick one card at random from a standard deck of 52 cards, what are the odds it will be an ace?
20. If you pick one card at random from a standard deck of 52 cards, what are the odds against drawing a face card?
21. If you pick one card at random from a standard deck of 52 cards, what are the odds it will not be a heart?
22. If you are given odds of 3 to 8 in favor of winning a bet, what is the probability of winning the bet?
23. If the odds against a given event are 2 to 7, what is the probability of the event occurring?
24. The odds of a student doing homework is 4 to 9. What is the probability of the student not doing homework?
25. The odds of it not raining are 5 to 2. What is the probability that it will not rain?
