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: A spinner has 6 equal regions. What is the probability of landing on yellow for the first spin and not landing on yellow for the second spin?

$$\frac{1}{6} \times \frac{5}{6}$$

Q: A bag contains 2 red and 4 blue marbles. What is the probability of drawing a blue marble, keeping it, then drawing a red marble?

$$\frac{4}{6} \times \frac{2}{5}$$

Q: At the peak of flu season, 10% of people get the flu. The test is positive 95% if the patient has flu, and 1% if not. If someone tests positive, what is the probability they have the flu?

$$\frac{0.95 \times 0.10}{0.95 \times 0.10 + 0.01 \times 0.90}$$

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 of winning with one ticket?

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

Question 1

A company has 3 quarters, 4 nickels, and 2 dimes in a coin purse. If a coin is picked at random, what is the probability that it is a quarter?

Accepted Answer

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

Question 2

When rolling a six-sided die, what is the 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

A drug trial for ADHD medication shows 10 improved with placebo, 30 improved with non-placebo, 40 improved total. What type of probability is $$\frac{40}{100}$$?

Accepted Answer

Marginal probability

Question 8

A spinner has 6 equal regions. What is the probability of landing on yellow for the first spin and not landing on yellow for the second spin?

Accepted Answer

$$\frac{1}{6} 	imes \frac{5}{6}$$

Question 9

A bag contains 2 red and 4 blue marbles. What is the probability of drawing a blue marble, keeping it, then drawing a red marble?

Accepted Answer

$$\frac{4}{6} 	imes \frac{2}{5}$$

Question 10

In a town, 15% have both a cat and a dog, and 64% have a dog. What is the probability that someone owns a cat given they have a dog?

Accepted Answer

$$\frac{0.15}{0.64}$$

Question 11

A rare condition affects 1 out of 100 people. The test is correct 95% if the person has the condition, and gives a false positive 10% if not. What is $$P(A|B)$$, where $$A is$$ 'tested positive' and $$B is$$ 'has condition'?

Accepted Answer

$$0.95$$

Question 12

At the peak of flu season, 10% of people get the flu. The test is positive 95% if the patient has flu, and 1% if not. If someone tests positive, what is the probability they have the flu?

Accepted Answer

$$\frac{0.95 	imes 0.10}{0.95 	imes 0.10 + 0.01 	imes 0.90}$$

Question 13

How many different meals can be made with 4 appetizers and 6 entrees?

Accepted Answer

$$4 	imes 6 = 24$$

Question 14

How many possible outcomes are there if you roll 5 dice?

Accepted Answer

$$6^5$$

Question 15

How many ways are there to arrange the letters in the word BANANA?

Accepted Answer

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

Question 16

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 17

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

Accepted Answer

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

Question 18

Which of the following best describes the difference between permutations and combinations?

Accepted Answer

Permutations: order matters; Combinations: order does not matter

Business Statistics: Introduction to Probability and Counting Principles

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