Q: A library randomly selects two books from a list of 100, with 62 fiction and 38 nonfiction. What is the probability both books are nonfiction?

$$\frac{38}{100} \times \frac{37}{99}$$

Q: You roll a six-sided die twice. What is the probability of rolling an even number on the first roll and a 3 on the second roll?

$$\frac{3}{6} \times \frac{1}{6} = \frac{1}{12}$$

Q: From a class of 28 students, in how many ways could a teacher select 4 students to lead the class discussion?

$$\frac{28!}{(28-4)! \times 4!}$$

Q: When playing a lottery game, you must choose 5 numbers between 1 and 40. What is the probability that you win with one ticket?

$$\frac{1}{\frac{40!}{(40-5)! \times 5!}}$$

Q: According to data from a metro station, 28% of trains are delayed. 73% of train delays and 35% of on-time rides were on days with precipitation. Given there is precipitation, what is the probability the train will be delayed?

$$\frac{0.73 \times 0.28}{0.73 \times 0.28 + 0.35 \times 0.72}$$

Q: How many different teams of 4 people can be formed from a group of 9 people?

$$\frac{9!}{(9-4)! \times 4!}$$

Question 1

A bag contains 3 quarters, 4 nickels, and 2 dimes. If you pick a coin at random, what is the probability that it will be a quarter?

Accepted Answer

$$\frac{3}{9}$$

Question 2

When rolling a six-sided die, what is the theoretical probability of rolling a number greater than 3?

Accepted Answer

$$\frac{1}{2}$$

Question 3

If the probability of rain tomorrow is 0.1 and the probability of snow is 0.25, what is the probability that it will not rain or snow?

Accepted Answer

$$1 - (0.1 + 0.25) = 0.65$$

Question 4

A card is drawn from a standard deck of 52 cards. What is the probability that the card is a diamond or a king?

Accepted Answer

$$\frac{13}{52} + \frac{4}{52} - \frac{1}{52} = \frac{16}{52}$$

Question 5

If two events A and B are mutually exclusive and $$P(A) = 0.15$$, $$P(B) = 0.32$$, what is $$P(A \cup B)$$?

Accepted Answer

$$0.15 + 0.32 = 0.47$$

Question 6

A library randomly selects two books from a list of 100, with 62 fiction and 38 nonfiction. What is the probability both books are nonfiction?

Accepted Answer

$$\frac{38}{100} 	imes \frac{37}{99}$$

Question 7

You roll a six-sided die twice. What is the probability of rolling an even number on the first roll and a 3 on the second roll?

Accepted Answer

$$\frac{3}{6} 	imes \frac{1}{6} = \frac{1}{12}$$

Question 8

A rare condition affects 1 out of every 100 people. The test is correct 95% of the time if the person has the condition, and gives a false positive 10% of the time if the person does not have the condition. What is $$P(	ext{tested positive} | 	ext{has condition})$$?

Accepted Answer

$$0.95$$

Question 9

How many different ways can you arrange the letters in the word BANANA?

Accepted Answer

$$\frac{6!}{3!2!1!}$$

Question 10

From a class of 28 students, in how many ways could a teacher select 4 students to lead the class discussion?

Accepted Answer

$$\frac{28!}{(28-4)! 	imes 4!}$$

Question 11

A menu lists 4 appetizers and 6 entrees. How many different meals with both an appetizer and an entree do you have to choose from?

Accepted Answer

$$4 	imes 6 = 24$$

Question 12

A student formed a club at their school. They have 13 members and need to elect a president, vice president, and treasurer. How many ways are there to fill these officer positions?

Accepted Answer

$$13 	imes 12 	imes 11$$

Question 13

You want to arrange 12 books on your bookshelf by color. If 4 are blue, 3 are yellow, and 5 are white, how many different ways could you arrange them?

Accepted Answer

$$\frac{12!}{4!3!5!}$$

Question 14

A company is hiring software developers and data analysts. Out of all applicants, 6 applied for software developer and 4 for data analyst. 4 of the software developer applicants have a degree in computer science and 2 of the analyst applicants have a degree in computer science. What is the probability that a randomly selected candidate with a degree in computer science applied for the software developer position?

Accepted Answer

Question 15

When playing a lottery game, you must choose 5 numbers between 1 and 40. What is the probability that you win with one ticket?

Accepted Answer

$$\frac{1}{\frac{40!}{(40-5)! 	imes 5!}}$$

Question 16

You conduct a survey of your statistics class with 40 students. 20 have a math major, 15 have a science major, and 8 have a double major in math & science. What is the probability that a randomly selected student has a math major, given that the student has a science major?

Accepted Answer

$$\frac{8}{15}$$

Question 17

According to data from a metro station, 28% of trains are delayed. 73% of train delays and 35% of on-time rides were on days with precipitation. Given there is precipitation, what is the probability the train will be delayed?

Accepted Answer

$$\frac{0.73 	imes 0.28}{0.73 	imes 0.28 + 0.35 	imes 0.72}$$

Question 18

How many different teams of 4 people can be formed from a group of 9 people?

Accepted Answer

$$\frac{9!}{(9-4)! 	imes 4!}$$

Chapter 5: Probability – Structured Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards