$$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$$

$$\sqrt{20 \times 0.4 \times 0.6}$$

Question 1

Which of the following best describes the probability of an event that is 'unlikely' according to the probability scale shown in the first image?

Accepted Answer

$$P(E) \leq 0.05$$

Question 2

Given the Venn diagram in the second image, which formula correctly represents the probability of 'A or B'?

Accepted Answer

$$P(A 	ext{ or } B) = P(A) + P(B) - P(A 	ext{ and } B)$$

Question 3

In the third image, what does the separation of the two circles represent in terms of probability events?

Accepted Answer

The events are disjoint (mutually exclusive)

Question 4

According to the fourth image, what is the probability of the complement of event $$A$$?

Accepted Answer

$$P(\overline{A}) = 1 - P(A)$$

Question 5

If you roll a fair six-sided die, as shown in the fifth image, what is the probability of rolling a number greater than 4?

Accepted Answer

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

Question 6

Based on the probability histogram in the sixth image, which of the following statements is true?

Accepted Answer

The most likely number of Mexican-American jurors among 12 is around 10.

Question 7

Which of the following is NOT a requirement for a probability distribution?

Accepted Answer

The random variable must be continuous.

Question 8

A multiple-choice test has 5 possible answers for each question. If you guess on one question, what is the probability of getting it wrong?

Accepted Answer

$$\frac{4}{5}$$

Question 9

If the probability of an event $$A is 0.2$$, what is the probability that $$A$$ does not occur?

Accepted Answer

$$0.8$$

Question 10

Suppose you have a binomial experiment with $$n = 10$$ and $$p = 0.3. $$What is the mean number of successes?

Accepted Answer

$$3$$

Question 11

In a binomial distribution with $$n = 20$$ and $$p = 0.4$$, what is the standard deviation?

Accepted Answer

$$\sqrt{20 	imes 0.4 	imes 0.6}$$

Question 12

A probability distribution is given by $$P(x) = \frac{1}{6}$$ for $$x = 1, 2, 3, 4, 5, 6. $$What is the mean $$\mu of $$this distribution?

Accepted Answer

$$3.5$$

Question 13

If the probability of a tire being defective is $$0.0003$$, what is the probability that at least one tire is defective in a lot of 100 tires?

Accepted Answer

$$1 - (1 - 0.0003$$)^{100}$$

Question 14

Which of the following is a correct formula for the number of ways to arrange 5 people in a line?

Accepted Answer

$$5!$$

Question 15

A committee of 3 is to be chosen from 7 people. How many different committees are possible?

Accepted Answer

$$\frac{7!}{3!4!}$$

Question 16

If $$P(A) = 0.3$$ and $$P(B) = 0.4$$ and $$A$$ and $$B$$ are disjoint, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.7$$

Question 17

If $$P(A) = 0.5$$, $$P(B) = 0.6$$, and $$P(A 	ext{ and } B) = 0.3$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.8$$

Question 18

A test consists of 10 true/false questions. If a student guesses on all questions, what is the probability of getting all answers correct?

Accepted Answer

$$\left(\frac{1}{2}\$$right)^{10}$$

Question 19

Which of the following is a property of a discrete random variable?

Accepted Answer

It can take on a countable number of values.

Probability and Probability Distributions: Core Concepts and Applications

Study Guide - Practice Questions