Q: A library randomly selects two books from a list of 62 fiction and 38 nonfiction books. What is the probability that both selected books are nonfiction (without replacement)?

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

Q: A test for a condition is positive 95% of the time when the condition is present and 1% of the time when it is not. If 10% of people have the condition, what is the probability that a randomly selected person who tests positive actually has the condition? (Use Bayes' Theorem.)

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

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

$$\frac{4}{6} \times \frac{2}{6} = \frac{8}{36} = \frac{2}{9}$$

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 nickel?

Accepted Answer

$$\frac{4}{9}$$

Question 2

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 3

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

Accepted Answer

$$\frac{5}{6}$$

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

$$\frac{16}{52}$$

Question 5

If $$P(A) = 0.15$$ and $$P(B) = 0.32$$ and A and B are mutually exclusive, 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 62 fiction and 38 nonfiction books. What is the probability that both selected books are nonfiction (without replacement)?

Accepted Answer

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

Question 7

A rare disease affects 1 out of every 100 people. The test for this disease is 95% accurate if the person has the disease, and 10% of healthy people test positive. What is $$P(	ext{positive} | 	ext{disease})$$?

Accepted Answer

$$0.95$$

Question 8

How many different ways can the letters in the word 'BANANA' be arranged?

Accepted Answer

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

Question 9

A teacher is choosing a president, vice president, and treasurer from 13 students. How many ways can these positions be filled?

Accepted Answer

$$13 	imes 12 	imes 11$$

Question 10

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

Accepted Answer

$$\frac{28!}{24!4!}$$

Question 11

A contingency table shows 40 seniors, 10 of whom drive a car, and 20 juniors, 30 of whom do not drive a car. What is the probability that a randomly selected student is a senior and drives a car?

Accepted Answer

$$\frac{10}{100}$$

Question 12

You flip a coin and roll a six-sided die. How many possible outcomes are there?

Accepted Answer

$$2 	imes 6 = 12$$

Question 13

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

Accepted Answer

Permutations consider order; combinations do not.

Question 14

A test for a condition is positive 95% of the time when the condition is present and 1% of the time when it is not. If 10% of people have the condition, what is the probability that a randomly selected person who tests positive actually has the condition? (Use Bayes' Theorem.)

Accepted Answer

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

Question 15

How many different 8-digit codes can be made using 5 zeros and 3 ones?

Accepted Answer

$$\frac{8!}{5!3!}$$

Question 16

If $$P(A) = 0.6$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.3$$, what is $$P(A \cup B)$$?

Accepted Answer

$$0.6 + 0.5 - 0.3 = 0.8$$

Question 17

A menu lists 4 appetizers and 6 entrees. How many different meals with both an appetizer and an entree are possible?

Accepted Answer

$$4 	imes 6 = 24$$

Question 18

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

Accepted Answer

$$\frac{4}{6} 	imes \frac{2}{6} = \frac{8}{36} = \frac{2}{9}$$

Question 19

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

Accepted Answer

$$\frac{9!}{5!4!}$$

Probability and Counting Rules – Study Notes (Triola, Elementary Statistics Ch. 4)

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