Question 1

Theoretical probability is the same as:

Accepted Answer

Theoretical probability is based on mathematical calculations and is determined from assumptions or theories. It is different from empirical or experimental probability, which is based on actual observed outcomes from an experiment or trial. Historical probability is also not the same as theoretical probability, as it refers to the frequency of past occurrences and is not necessarily based on mathematical calculations. Therefore, option C (mathematical probability) is the best choice.

Question 2

Sundaes at an ice cream shop have either vanilla or chocolate ice cream; marshmallow, strawberries, or hot fudge for toppings; and either a cherry or peanuts as a garnish. How many sundae combinations are possible?

Accepted Answer

B

Question 3

A bag has 6 green marbles and 3 blue marbles. You pick out a blue marble. If you do not put the marble back, what is the probability of now selecting a green marble?

Accepted Answer

Since one blue marble has already been drawn and not replaced, there are now only 2 blue marbles and a total of 8 marbles left in the bag. Therefore, the probability of selecting a green marble is 6/8 or 3/4, which is option C.

Question 4

What is the odds in favor of rolling a 7 with a pair of dice?

Accepted Answer

There are 6 ways to roll a 7 out of the 36 possible outcomes when rolling a pair of dice. The odds in favor can be expressed as 6 favorable outcomes out of 36 total outcomes, which simplifies to 6/36 or 1/6. Option B, which is 6:30, simplifies to 1:5 and represents the odds against rolling a 7, not in favor of rolling a 7. Therefore, option B is the best choice for the odds in favor of rolling a 7.

Question 5

All of the following are true of a fair spinner except that it:

Accepted Answer

The answer of All of the following are true of...

Question 6

When conducting a sample of a population:

Accepted Answer

A relatively small random sample can provide accurate information about the entire population as long as the sample is representative and randomly selected. The size of the sample needed depends on the size of the overall population and the level of precision desired in the results, but it is not necessary to sample the entire population or draw multiple samples to make inferences.

Question 7

What is the probability that a day in the month of March has a 2 in it?

Accepted Answer

The answer of What is the probability that a day...

Question 8

Which of the following is a true statement concerning probability values?

Accepted Answer

The answer of Which of the following is a true...

Question 9

Determining the probability that your insurance rates will be higher than others is based on:

Accepted Answer

The answer of Determining the probability that your insurance rates...

Question 10

The law of large numbers stipulates that

Accepted Answer

The law of large numbers states that as the number of events increases, the actual probability of the events will approach the theoretical probability. This means that the more times an experiment is performed, the closer the observed results will be to the expected results.

Question 11

A 40% chance of snow means the probability of snow is:

Accepted Answer

The answer of A 40% chance of snow means the...

Question 12

What is the probability of rolling a 6 with a pair of dice?

Accepted Answer

The answer of What is the probability of rolling a...

Question 13

What is the sum of the numbers in the fourth row of Pascal's Triangle?

Accepted Answer

Pascal's Triangle starts with a 1 at the top. Each row thereafter consists of numbers that are the sum of the two numbers directly above. The fourth row of Pascal's Triangle is 1, 3, 3, 1, and the sum of these numbers is 8.

Question 14

A student took the letters M, A, T and wrote down the possibilities MAT, MTA, TAM, TMA, ATM, AMT from the given three letters. When the student wrote out the 6 possibilities, he was finding the

Accepted Answer

The student is finding the permutations of the letters M, A, T, which means he is listing out all possible orders in which these letters can be arranged. Therefore, the best choice is D, permutations of M, A, T.

Question 15

Empirical probability is used in which of the following?

Accepted Answer

Empirical probability is based on actual data and observations, and is often used to determine insurance rates based on past occurrences of certain events (such as car accidents or medical conditions). It is not typically used in games of chance like lottery, slot machines, or roulette, which rely on theoretical probabilities.

Question 16

A fair spinner with four colors on its face must have the following be true except:

Accepted Answer

A spinner with four colors may have more than one region for each color. For example, the color blue could have two separate regions on the face of the spinner. Therefore, Choice C is not necessarily true for all fair spinners with four colors.

Question 17

Suppose a spinner is divided into 4 areas: $6 (geometric probability of ½), $4 (geometric probability of ¼), $2 (geometric probability of ⅛ for each ⅛ section). How much would an organization have to charge in order to break even?

Accepted Answer

The answer of Suppose a spinner is divided into 4...

Question 18

Children who are susceptible to the gambler's fallacy believe that:

Accepted Answer

Children who are susceptible to the gambler's fallacy believe that if they have a streak of one outcome, the opposite is more likely to occur on the next trial. This is why they may think a tail is "due" if they have had a long streak of heads.

Question 19

The outcome when tossing one coin is (H, T).  The outcome when tossing two coins is (HH, HT, TH, TT). The outcome when tossing three coins is (HHH, HHT, HTH, THH, TTH, THT, HTT, TTT). This pattern of outcomes can be mapped to:

Accepted Answer

The outcomes of tossing coins follow the same pattern as Pascal's Triangle, where each outcome is the sum of the two outcomes directly above it. For example, HHT is the sum of HH and HT in the previous row. Therefore, Pascal's Triangle is the best choice to map the outcomes of tossing coins.

Question 20

Simulations are used to determine the probability of an event in all of the following situations except for :

Accepted Answer

Simulations are not needed when the theoretical probability is available because it can be directly calculated. Simulations are primarily used when there is no other way to estimate the probability of an event, such as when no data exists or the theoretical probability is impossible to compute.

Quiz 19: Investigating Probability