Question 1

According to the Law of Large Numbers, what happens to the relative frequency of an event as the number of trials increases?

Accepted Answer

It approaches the theoretical probability of the event.

Question 2

A random process is best described as:

Accepted Answer

A process where the outcome is unpredictable, but the proportion of outcomes stabilizes over many trials.

Question 3

If you roll a fair six-sided die 600 times, what is the expected number of times you will roll a '4'?

Accepted Answer

$$100$$

Question 4

Which of the following is an example of an empirical probability?

Accepted Answer

Estimating the probability of rain tomorrow based on weather data from the past 10 years.

Question 5

Suppose you have a bag with 3 red, 2 blue, and 5 green marbles. If you randomly select one marble, what is the probability it is blue?

Accepted Answer

$$\frac{2}{10}$$

Question 6

A probability model must satisfy which of the following rules?

Accepted Answer

The probability of any event must be between 0 and 1, inclusive.

Question 7

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

Accepted Answer

The sample space.

Question 8

If the probability of an event is 0.03, how would you classify this event?

Accepted Answer

An unusual event.

Question 9

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

Accepted Answer

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

Question 10

Which of the following best describes the difference between the Law of Large Numbers and the (nonexistent) Law of Averages?

Accepted Answer

The Law of Averages states that outcomes will 'even out' in the short run, while the Law of Large Numbers states that relative frequencies stabilize in the long run.

Question 11

If an event is impossible, what is its probability?

Accepted Answer

$$0$$

Question 12

You flip a fair coin three times. What is the probability of getting exactly two heads?

Accepted Answer

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

Question 13

In a probability experiment, what is an 'event'?

Accepted Answer

Any collection of outcomes from the sample space.

Question 14

A probability model for a bag of candies shows the following probabilities: Brown: 0.12, Yellow: 0.15, Red: 0.23, Blue: 0.23, Green: 0.15. What is the probability of drawing a color that is not red?

Accepted Answer

$$0.77$$

Question 15

If you observe the outcome 'side with dot' 1344 times out of 3939 trials in a pig-rolling experiment, what is the empirical probability of this outcome?

Accepted Answer

$$\frac{1344}{3939}$$

Question 16

Which of the following statements about probability is FALSE?

Accepted Answer

The probability of any event can be greater than 1.

Question 17

Suppose you conduct an experiment where you record whether a traffic light is red or not for 200 days. If the light is red on 123 days, what is the empirical probability of being stopped by the red light?

Accepted Answer

$$\frac{123}{200}$$

Question 18

If the probability of an event is 0.65, how many times would you expect the event to occur in 100 trials?

Accepted Answer

$$65$$

Question 19

Which of the following is NOT a property of probability?

Accepted Answer

The probability of an event can be negative.

Question 20

If you roll a fair 10-sided die, what is the probability of rolling a '4'?

Accepted Answer

$$\frac{1}{10}$$

Probability Rules and Random Processes: Study Notes for Statistics

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