Q: A library randomly selects two books from a list of 100 books (62 fiction, 38 nonfiction). What is the probability that both books selected 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 lottery game requires you to choose 5 numbers between 1 and 40. What is the probability of winning with one ticket?

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

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 flip a coin and roll a six-sided die, how many possible outcomes are there?

Accepted Answer

$$2 	imes 6 = 12$$

Question 8

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

Accepted Answer

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

Question 9

A rare disease affects 1 out of every 100 people. The test for this disease is correct 95% of the time if the person has the disease, and gives a false positive 10% of the time if the person does not have the disease. What is $$P(A|B)$$, the probability of testing positive given the person has the disease?

Accepted Answer

$$0.95$$

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

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 13

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

$$\frac{4}{6+2}$$

Question 14

You roll 5 dice. How many possible outcomes are there?

Accepted Answer

$$6^5$$

Question 15

A lottery game requires you to choose 5 numbers between 1 and 40. What is the probability of winning with one ticket?

Accepted Answer

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

Question 16

What is the difference between permutations and combinations?

Accepted Answer

Permutations are used when order matters; combinations are used when order does not matter.

Question 17

A contingency table shows the results from a drug trial for a new ADHD medication. If 10 out of 50 placebo group participants' symptoms improved, what type of probability is this?

Accepted Answer

Joint probability

Question 18

According to Bayes' Theorem, which formula correctly calculates $$P(B|A)$$?

Accepted Answer

$$\frac{P(A|B) \cdot P(B)}{P(A|B) \cdot P(B) + P(A|B') \cdot P(B')}$$

Probability and Counting Principles – Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards