Question 1

Which of the following best describes the Law of Large Numbers?

Accepted Answer

As the number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to the probability of the outcome.

Question 2

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

Accepted Answer

$$\frac{6}{30} = 0.2$$

Question 3

Which of the following is an example of a subjective probability?

Accepted Answer

An economist predicts a 20% chance of recession next year based on their judgment.

Question 4

In a probability experiment, the sample space $$S$$ consists of 4 outcomes: $$e_1$$, $$e_2$$, $$e_3$$, $$e_4. If$$ $$P(e_1$) = 0.2$$, $$P(e_2$) = 0.3$$, $$P(e_3$) = 0.1$$, what must $$P(e_4$) be $$for this to be a valid probability model?

Accepted Answer

$$0.4$$

Question 5

A class of 52 students rolled pigs 3,939 times in the game Pass the Pigs. The 'Leaning Jowler' outcome occurred 32 times. What is the empirical probability of this outcome?

Accepted Answer

$$\frac{32}{3939} \approx 0.008$$

Question 6

Which of the following statements about probability is FALSE?

Accepted Answer

The probability of any event can be less than 0.

Question 7

Suppose a survey of 500 families with three children found that 180 had two boys and one girl. What is the empirical probability that a randomly selected family has two boys and one girl?

Accepted Answer

$$\frac{180}{500} = 0.36$$

Question 8

If an event is certain to occur, what is its probability?

Accepted Answer

$$1$$

Question 9

A coin is flipped 100 times. The proportion of heads after each flip is plotted. According to the Law of Large Numbers, what should happen to the proportion of heads as the number of flips increases?

Accepted Answer

It should get closer to 0.5.

Question 10

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

Accepted Answer

Each probability must be greater than 1.

Question 11

Suppose you roll a fair six-sided die. What is the probability of rolling a number greater than 4?

Accepted Answer

$$\frac{2}{6} = \frac{1}{3}$$

Question 12

A probability experiment consists of tossing a coin three times. What is the sample space $$S$$?

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

A probability model for the colors of M&Ms in a bag is given as: 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 their sum is 1.

Question 15

Which of the following best describes an unusual event?

Accepted Answer

An event that has a low probability of occurring.

Question 16

A family has three children. Assuming boys and girls are equally likely, what is the probability that the family has exactly two boys and one girl (in any order)?

Accepted Answer

$$\frac{3}{8} = 0.375$$

Question 17

Which of the following is an example of a random process?

Accepted Answer

Flipping a fair coin and recording heads or tails.

Question 18

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

Accepted Answer

The event is impossible.

Chapter 5: Probability – Rules, Methods, and Applications

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