Q: If 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?

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

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

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

Q: At the peak of flu season, 10% of people in a town get sick with the flu. The test is positive 95% of the time given the patient has flu and 1% of the time given they do not have the flu. If someone tests positive, what is the probability that they have the flu? (Use Bayes' Theorem)

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

Question 1

A six-sided die is rolled. What is the theoretical probability of rolling a number greater than 3?

Accepted Answer

$$\frac{3}{6}$$

Question 2

In a bag containing 3 quarters, 4 nickels, and 2 dimes, what is the probability of randomly selecting a quarter?

Accepted Answer

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

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

$$0.65$$

Question 4

When drawing a single card from a standard deck of 52 cards, what is the probability that you will NOT draw a queen?

Accepted Answer

$$\frac{48}{52}$$

Question 5

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

Accepted Answer

$$0.47$$

Question 6

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

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

Question 7

If 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

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

Question 8

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

Accepted Answer

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

Question 9

In a survey of 40 students, 20 have a math major, 15 have a science major, and 8 have both. What is the probability that a randomly selected student has a math major, given they have a science major?

Accepted Answer

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

Question 10

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 $$P(A|B)$$, the probability of testing positive given the person has the condition?

Accepted Answer

$$0.95$$

Question 11

At the peak of flu season, 10% of people in a town get sick with the flu. The test is positive 95% of the time given the patient has flu and 1% of the time given they do not have the flu. If someone tests positive, what is the probability that they have the flu? (Use Bayes' Theorem)

Accepted Answer

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

Question 12

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

Accepted Answer

$$6^5$$

Question 13

How many options are there for license plates with any 3 letters (A-Z) followed by any 3 numbers (0-9)?

Accepted Answer

$$26^3$$ 	imes $$10^3$$

Question 14

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

Accepted Answer

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

Question 15

A teacher is choosing a president, vice president, and treasurer from a club of 13 members. How many ways are there to fill these officer positions?

Accepted Answer

$$13 	imes 12 	imes 11$$

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

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

Question 17

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

Accepted Answer

$$\frac{1}{\frac{40!}{35!5!}}$$

Question 18

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

Accepted Answer

Permutations: order matters; Combinations: order does not matter

Probability and Counting Principles – Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard