Q: A door passcode uses four digits. The second digit must be 4, and the last digit must be even. How many different passcodes are possible if digits can repeat?

$$10 \times 1 \times 10 \times 5 = 500$$

Q: Which formula is used to calculate the probability of an event $$A$$?

$$P(A) = \displaystyle \frac{\text{number of occurrences of } A}{\text{total number of outcomes}}$$

Question 1

Which of the following best describes the Rare Event Rule for Inferential Statistics?

Accepted Answer

If, under a given assumption, the probability of an observed event is extremely small, then the assumption is probably not correct.

Question 2

What is the sample space for flipping a coin twice?

Accepted Answer

HH, HT, TH, TT

Question 3

Which of the following numbers cannot be a probability?

Accepted Answer

$$-0.2938$$

Question 4

A password consists of five different capital letters. How many possible passwords can be formed?

Accepted Answer

$$\displaystyle \frac{26!}{21!}$$

Question 5

If you roll a six-sided die and flip a coin, how many possible outcomes are there?

Accepted Answer

$$12$$

Question 6

Which of the following best describes classical probability?

Accepted Answer

Probability calculated when each event has an equal chance of occurring, without actually performing the experiment.

Question 7

What is the value of $$5! ($$five factorial)?

Accepted Answer

$$120$$

Question 8

A door passcode uses four digits. The second digit must be 4, and the last digit must be even. How many different passcodes are possible if digits can repeat?

Accepted Answer

$$10 	imes 1 	imes 10 	imes 5 = 500$$

Question 9

Which of the following statements about probability is FALSE?

Accepted Answer

If the probability of an event is zero, the event is certain.

Question 10

You are buying a car. There are 3 manufacturers (Ford, GM, Honda), 2 car sizes (compact, midsize), and 4 colors (white, red, black, green). How many different ways can you select one manufacturer, one car size, and one color?

Accepted Answer

$$3 	imes 2 	imes 4 = 24$$

Question 11

Which formula is used to calculate the probability of an event $$A$$?

Accepted Answer

$$P(A) = \displaystyle \frac{	ext{number of occurrences of } A}{	ext{total number of outcomes}}$$

Question 12

If you have 4 shirts, 3 pairs of pants, and 3 pairs of shoes, how many different outfits can you make (choosing one of each)?

Accepted Answer

$$4 	imes 3 	imes 3 = 36$$

Question 13

Which of the following is a simple event?

Accepted Answer

Flipping a coin and getting heads

Question 14

Which of the following best describes the Fundamental Counting Principle?

Accepted Answer

Multiply the number of possible outcomes for each part of a procedure.

Question 15

Which of the following is an example of a dependent event?

Accepted Answer

Selecting a king from a deck, not replacing it, then selecting a queen.

Question 16

If you flip a coin, spin a spinner with 3 colors, and flip another coin, how many possible outcomes are there?

Accepted Answer

$$2 	imes 3 	imes 2 = 12$$

Question 17

Which of the following is NOT a property of probability?

Accepted Answer

A probability can be greater than 1.

Question 18

Which of the following best describes a sample space?

Accepted Answer

The set of all possible outcomes of a procedure.

Question 19

What is the value of $$0! ($$zero factorial)?

Accepted Answer

$$1$$

Question 20

Which of the following is an example of relative frequency probability?

Accepted Answer

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

Introductory Statistics: Chapter 4 – Probability

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