Q: If two events $$E$$ and $$F$$ are independent, which formula gives the probability that both $$E$$ and $$F$$ occur?

$$P(E \text{ and } F) = P(E) \times P(F)$$

Question 1

A fair six-sided die is rolled once. What is the probability of rolling a number greater than 4?

Accepted Answer

$$\frac{1}{3}$$

Question 2

Which of the following statements best describes the Law of Large Numbers (LLN)?

Accepted Answer

As the number of repetitions of a probability experiment increases, the observed proportion of an outcome gets closer to the theoretical probability.

Question 3

A bag contains 9 brown, 6 yellow, 7 orange, 4 red, 2 blue, and 2 green candies. If one candy is selected at random, what is the probability that it is either yellow or blue?

Accepted Answer

$$\frac{8}{30}$$

Question 4

Which of the following cannot be the probability of an event?

Accepted Answer

1.2

Question 5

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

Accepted Answer

$$0.7$$

Question 6

A card is drawn from a standard deck of 52 cards. What is the probability that it is either a king or a club?

Accepted Answer

$$\frac{17}{52}$$

Question 7

Which of the following is an example of subjective probability?

Accepted Answer

An economist predicts there is a 20% chance of recession next year.

Question 8

If two events $$E$$ and $$F$$ are independent, which formula gives the probability that both $$E$$ and $$F$$ occur?

Accepted Answer

$$P(E 	ext{ and } F) = P(E) 	imes P(F)$$

Question 9

A survey found that 31.6% of households own a dog. What is the probability that a randomly selected household does NOT own a dog?

Accepted Answer

$$0.684$$

Question 10

A coin is flipped and a die is rolled. What is the probability of getting a head and a 5?

Accepted Answer

$$\frac{1}{12}$$

Question 11

Which of the following best describes a sample space?

Accepted Answer

A collection of all possible outcomes of an experiment.

Question 12

If the probability of an event $$E is$$ $$0$$, what can be said about $$E$$?

Accepted Answer

Event $$E is $$impossible.

Question 13

A die is rolled. What is the probability of getting a number less than or equal to 4?

Accepted Answer

$$\frac{2}{3}$$

Question 14

Which of the following is NOT a property of probability?

Accepted Answer

The probability of an event can be negative.

Question 15

A company has 309 employees who travel 10-19 miles, 257 who travel 20-29 miles, 78 who travel 30-39 miles, and 2 who travel 40-49 miles to work. If one employee is selected at random, what is the probability that the employee travels between 10 and 29 miles?

Accepted Answer

$$\frac{566}{646}$$

Question 16

If $$P(E) = 0.4$$ and $$P(F) = 0.5$$ and $$E$$ and $$F$$ are mutually exclusive, what is $$P(E 	ext{ or } F)$$?

Accepted Answer

$$0.9$$

Question 17

A card is drawn from a deck, replaced, and then a second card is drawn. What is the probability of getting a queen and then an ace?

Accepted Answer

$$\frac{1}{169}$$

Question 18

Which method of computing probability is based on the long-run relative frequency of an event's occurrence?

Accepted Answer

Empirical method

Question 19

If the probability of a randomly selected Hartford resident having a commute time more than 90 minutes is $$0.012$$, what is the probability that a resident has a commute time less than 90 minutes?

Accepted Answer

$$0.988$$

Question 20

If $$P(E) = 0.4$$, $$P(F) = 0.5$$, and $$P(E 	ext{ and } F) = 0.2$$, what is $$P(E 	ext{ or } F)$$?

Accepted Answer

$$0.7$$

Chapter 5: Probability – Foundations, Models, and Rules

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