Q: Which formula represents the empirical probability of an event $$E$$?

$$P(E) \approx \frac{\text{frequency of } E}{\text{number of trials of experiment}}$$

Question 1

Which of the following best describes a random event in statistics?

Accepted Answer

An event where the outcome is uncertain, but a definite distribution of outcomes would emerge if repeated many times under identical conditions.

Question 2

According to the Law of Large Numbers, what happens as the number of repetitions of a probability experiment increases?

Accepted Answer

The observed proportion of an outcome gets closer to the probability of the outcome.

Question 3

A bag contains 9 brown, 6 yellow, 7 red, 4 orange, 2 blue, and 2 green M&Ms. What is the probability of randomly selecting a yellow M&M?

Accepted Answer

$$\frac{6}{30}$$

Question 4

Which of the following is NOT a requirement for a valid probability model?

Accepted Answer

Each outcome must have a different probability.

Question 5

If you toss a fair coin three times, what is the probability of getting exactly two heads?

Accepted Answer

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

Question 6

A class rolled a pig 3,939 times in the game 'Pass the Pigs.' The pig landed on 'Leaning Jowler' 32 times. What is the empirical probability of this outcome?

Accepted Answer

$$\frac{32}{3939}$$

Question 7

Suppose you randomly select two people from a group of four (Juhi, Ashwin, Ramon, Destiny) to attend a concert. What is the probability that Juhi is selected?

Accepted Answer

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

Question 8

Which of the following statements about probability is TRUE?

Accepted Answer

Probability is a measure of the likelihood of a random phenomenon or chance behavior.

Question 9

In the classical method, if an experiment has $$n$$ equally likely outcomes and an event $$E$$ can occur in $$m$$ ways, what is the probability of $$E$$?

Accepted Answer

$$P(E) = \frac{m}{n}$$

Question 10

A family with three children is surveyed. Assuming boys and girls are equally likely, what is the probability that the family has exactly two boys and one girl?

Accepted Answer

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

Question 11

Which of the following is an example of an unusual event?

Accepted Answer

An event with a probability close to 0.

Question 12

If the probability of an event $$E is 0$$, what does this mean?

Accepted Answer

The event is impossible.

Question 13

A probability model for the color of M&Ms in a bag gives the following probabilities: Brown 0.12, Yellow 0.15, Red 0.12, Blue 0.23, Orange 0.23, Green 0.15. Is this a valid probability model?

Accepted Answer

Yes, because all probabilities are between 0 and 1 and sum to 1.

Question 14

Which formula represents the empirical probability of an event $$E$$?

Accepted Answer

$$P(E) \approx \frac{	ext{frequency of } E}{	ext{number of trials of experiment}}$$

Question 15

If you toss a fair six-sided die 10,000 times, what would you expect about the proportion of times a '3' appears?

Accepted Answer

It will be close to $$\frac{1}{6}.$$

Question 16

A probability model assigns a probability of 0.008 to an event. In 1000 repetitions, about how many times would you expect this event to occur?

Accepted Answer

8

Question 17

Which of the following best describes the sample space for tossing a fair coin three times?

Accepted Answer

$$\{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$$

Question 18

In a probability experiment, the set of all possible outcomes is called:

Accepted Answer

Sample space

Question 19

If the probability of selecting a yellow M&M is 0.2 and a blue M&M is 0.067, how many times more likely is it to select a yellow than a blue?

Accepted Answer

Three times as likely

Question 20

A survey of 500 families with three children found that 180 had two boys and one girl. What is the empirical probability of this event?

Accepted Answer

$$\frac{180}{500}$$

Introduction to Probability: Concepts, Models, and Methods

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