Question 1

Which of the following statements best describes the probability of an event A, where $$P(A) = 0.5$$?

Accepted Answer

Event A is equally likely to occur or not occur.

Question 2

A fair six-sided die is rolled. What is the probability of rolling an even number?

Accepted Answer

$$\frac{1}{2}$$

Question 3

Which of the following is a requirement for a discrete probability distribution?

Accepted Answer

$$0 \leq P(x) \leq 1$$ for all x$

Question 4

If you flip three fair coins, what is the probability of getting exactly two heads?

Accepted Answer

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

Question 5

A roulette wheel has 38 slots (numbers 1-36, 0, and 00). If you bet $1 on a single number, what is the expected value of your winnings?

Accepted Answer

$$E(x) = -0.05$$

Question 6

Which of the following best describes mutually exclusive events?

Accepted Answer

Events that have no overlap and cannot occur together.

Question 7

Given the following joint probability table for beer drinking and gender, what is the probability that a randomly selected individual is a female beer drinker?

Accepted Answer

$$0.175$$

Question 8

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

Accepted Answer

$$0.12$$

Question 9

A deck of 52 cards contains 4 aces. What is the probability of drawing an ace or a heart from a well-shuffled deck?

Accepted Answer

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

Question 10

If $$P(A) = 0.7$$, $$P(B) = 0.4$$, and $$P(A 	ext{ and } B) = 0.2$$, what is $$P(B|A)$$?

Accepted Answer

$$0.2857$$

Question 11

Which formula correctly calculates the expected value $$E(x)$$ for a discrete random variable?

Accepted Answer

$$E(x) = \sum xP(x)$$

Question 12

A lottery ticket costs $$2. There is a 1 in 1,000,000 chance to win 1$$,000,000 and a 1 in 500,000 chance to win $10,000. What is the expected value of buying one ticket?

Accepted Answer

$$-0.99$$

Question 13

Which of the following is an example of a continuous random variable?

Accepted Answer

The distance a car travels on a tank of gas

Question 14

If $$P(A|B) = P(A)$$, what does this imply about events A and B?

Accepted Answer

A and B are independent.

Question 15

In a game, you have a 1/3 chance to win $$300, a 1/3 chance to win 120$$, and a 1/3 chance to win nothing. What is the expected value of your winnings?

Accepted Answer

$$140$$

Question 16

Which of the following best describes collectively exhaustive events?

Accepted Answer

Events that together include all possible outcomes.

Question 17

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

Accepted Answer

$$0.8$$

Question 18

A random variable $$x$$ has the following probability distribution: $$x = 0, 1, 2$$ with $$P(x) = 0.2, 0.5, 0.3$$ respectively. What is the expected value $$E(x)$$?

Accepted Answer

$$1.1$$

Question 19

Which of the following is NOT a property of probability?

Accepted Answer

$$P(A) \u003e 1 is $$possible for some events

Probability Concepts and Discrete Probability Distributions: Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard