Section PC.5 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 |
Suppose a student is chosen at random:
- a. Find the probability that the student is female and earned an A.
- b. Find the probability that the student is male and earned an A.
- c. Find the probability that the student is male or earned a C.
- d. Find the probability that the student is female or earned a B
2. The table below shows the number of credit cards owned by a group of individuals.
| Zero Cards | One Card | Two+ Cards | Total | |
|---|---|---|---|---|
| Male | 9 | 5 | 19 | 33 |
| Female | 18 | 10 | 20 | 48 |
| Total | 27 | 15 | 39 | 81 |
Suppose a person is chosen at random:
- a. Find the probability that the person is male and has two+ credit cards.
- b. Find the probability that the person is female and has one credit card.
- c. Find the probability that the person is male or has no credit cards.
- d. Find the probability that the person is female or has no credit cards.
3. Suppose we draw one card from a standard deck. What is the probability of drawing the King of hearts or a Queen?
4. Suppose you roll a six-sided die. What is the probability that you roll an even number or a five?
5. Suppose we draw one card from a standard deck. What is the probability of drawing a King or a heart?
6. Suppose we draw one card from a standard deck. What is the probability of drawing a face card or a diamond?
7. Suppose we draw one card from a standard deck. What is the probability of drawing a Jack or a black card?
8. Two six-sided dice are rolled. What is the probability of getting a sum of either 11 or 12?
9. A jar contains 6 red marbles numbered 1 to 6 and 8 blue marbles numbered 1 to 8. A marble is drawn at random from the jar. Find the probability the marble is red or odd-numbered.
10. A jar contains 4 red marbles numbered 1 to 4 and 10 blue marbles numbered 1 to 10. A marble is drawn at random from the jar. Find the probability the marble is blue or even-numbered.
11. A jar contains 4 red marbles numbered 1 to 4 and 12 blue marbles numbered 1 to 12. A marble is drawn at random from the jar. Find the probability of the given event.
a. The marble is red or odd-numbered
b. The marble is blue and even-numbered
12. Given the following information, determine P(A or B).
P(A) = 0.56
P(B) = 0.53
P(A and B) = 0.42
P(B|A) = 0.3
13. Given the following information, determine P(A or B).
P(A) = 0.76
P(B) = 0.3
P(A and B) = 0.28
P(B|A) = 0.2
14. A glass jar contains 1 red, 3 green, 2 blue, and 4 yellow marbles. If a single marble is chosen at random from the jar, what is the probability that it is yellow or green?
15. A day of the week is chosen at random. What is the probability of choosing a Monday or Tuesday?
16. 22 customers are eating dinner at an Italian restaurant. Of the 22 customers, 18 order pizza, 10 order a salad, and 8 order pizza and salad. Using this information, answer each of the following questions. Let A be the event that a randomly selected customer orders pizza and B be the event that a randomly selected customer orders a salad.
- a. What is P(A), the probability that a customer orders pizza?
- b. What is P(B), the probability that a customer orders salad?
- c. What is P(A and B), the probability that a customer orders pizza and salad?
- d. What is P(A or B), the probability that a customer orders pizza or a salad?
17. On New Year’s Eve, the probability of a person having a car accident is 0.15. The probability of a person driving while intoxicated is 0.32. The probability of a person having a car accident and driving while intoxicated is 0.09. What is the probability of a person driving while intoxicated or having a car accident?
18. In a statistics class there are 18 juniors and 10 seniors; 6 of the seniors are females and 12 of the juniors are males. If a student is selected at random, find the probability of selecting the following:
- a. P(a junior or a female)
- b. P(a junior or a senior)
19. It is equally probable that the pointer on the spinner shown will land on any one of the regions. If the pointer land on a borderline, spin again. Find the probability that the pointer will stop on a red or blue region.
20. A recent study of 200 nurses found that of 125 female nurses, 56 had bachelor’s degrees; and of 75 male nurses, 34 had bachelor’s degrees. If a nurse is selected at random, find the probability that the nurse is:
- a. a female nurse with a bachelor’s degree
- b. a male nurse
- c. a male nurse with a bachelor’s degree
- d. based on your answer to a, b, and c, explain which is most likely to occur. Why?
21. Below is a list of all possible outcomes in the experiment of rolling two die.
| Die Roll Outcomes | |||||
|---|---|---|---|---|---|
| 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 |
Determine the following probabilities. Write answer as simplified fraction.
- a. P( sum is odd)
- b. P( sum is odd)
- c. P( sum is 7)
- d. P( sum is 7 and at least one of the die is a 1)
- e. P( sum is 7 or at least one of the die is a 1)
22. A survey was conducted at a local ballroom dance studio asking 86 students if they had ever competed in the following dance categories: Smooth, Rhythm, or Standard. The results were then presented to the owner in the following Venn Diagram.
Determine the following probabilities. Write your answers in percent form, rounded to the nearest tenth.
- a. P(Smooth)
- b. P(Rhythm and Standard)
- c. P(Smooth or Standard)
- d. P(not Smooth)
