Q: A bag contains 2 red and 4 blue marbles. If you draw one marble, keep it, and then draw another, what is the probability both are blue?

$$\frac{4}{6} \times \frac{3}{5} = \frac{2}{5}$$

Q: A phone number is 10 digits long. If the first and fourth digits cannot be 0, how many possible phone numbers are there?

$$9 \times 10^2$ \times 9 \times 10^6$

Question 1

A bag contains 3 red marbles and 5 blue marbles. If you randomly select one marble, what is the probability that it is red?

Accepted Answer

$$\frac{3}{8}$$

Question 2

Which of the following best describes empirical probability?

Accepted Answer

Probability calculated based on observed outcomes from an experiment.

Question 3

If $$P(A) = 0.3$$, what is the probability of the complement of event $$A$$?

Accepted Answer

$$0.7$$

Question 4

A weather report states there is a 20% chance of rain and a 10% chance of snow tomorrow. What is the probability that it will NOT rain or snow?

Accepted Answer

$$1 - (0.2 + 0.1) = 0.7$$

Question 5

When rolling a six-sided die, what is the probability of rolling a number greater than 4?

Accepted Answer

$$\frac{2}{6}$$

Question 6

Which of the following pairs of events are mutually exclusive?

Accepted Answer

Getting heads and getting tails on a single coin flip.

Question 7

If $$P(A) = 0.4$$ and $$P(B) = 0.3$$ and $$A$$ and $$B$$ are mutually exclusive, what is $$P(A \cup B)$$?

Accepted Answer

$$0.4 + 0.3 = 0.7$$

Question 8

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 9

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

Accepted Answer

$$2 	imes 6 = 12$$

Question 10

A bag contains 2 red and 4 blue marbles. If you draw one marble, keep it, and then draw another, what is the probability both are blue?

Accepted Answer

$$\frac{4}{6} 	imes \frac{3}{5} = \frac{2}{5}$$

Question 11

A contingency table shows 60 students, 40 of whom drive a car. What is the marginal probability that a randomly selected student drives a car?

Accepted Answer

$$\frac{40}{60}$$

Question 12

A rare disease affects 1 out of every 100 people. The test for the disease is 95% accurate if you have the disease, and 10% false positive if you do not. What is $$P(B')$$, the probability a person does NOT have the disease?

Accepted Answer

$$0.99$$

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

$$13 	imes 12 	imes 11$$

Question 15

Which formula is used to calculate the number of combinations of $$n$$ objects taken $$r at a $$time?

Accepted Answer

$$\frac{n!}{(n-r)!r!}$$

Question 16

A phone number is 10 digits long. If the first and fourth digits cannot be 0, how many possible phone numbers are there?

Accepted Answer

$$9 	imes 10^2$ 	imes 9 	imes 10^6$

Question 17

Which of the following scenarios involves a combination rather than a permutation?

Accepted Answer

Selecting 4 students from a class of 28 to lead a discussion.

Question 18

If $$P(A \cap B) = 0.12$$ and $$P(A) = 0.3$$, what is $$P(B|A)$$?

Accepted Answer

$$\frac{0.12}{0.3} = 0.4$$

Question 19

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

Accepted Answer

Probability: Basic Concepts, Rules, and Counting Principles

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