Question 1

Two outcomes are said to be mutually exclusive when

Accepted Answer

Mutually exclusive outcomes cannot occur together, meaning the probability of both events occurring simultaneously is zero.

Question 2

A gambler rolls a 3 with one roll of a single fair die.Given that the die was six-sided,what was the probability of rolling a 3 with one roll?

Accepted Answer

A fair die has 6 equally likely outcomes, and rolling a 3 is one of them. Therefore, the probability of rolling a 3 with one roll of a fair die is 1/6.

Question 3

Which rule states that when two outcomes are mutually exclusive,the probability that either one of these outcomes will occur is the sum of their individual probabilities?

Accepted Answer

The additive rule states that if two events are mutually exclusive, meaning they cannot occur simultaneously, then the probability of either event occurring is the sum of their individual probabilities. This is expressed as P(A or B) = P(A) + P(B). Therefore, choice A is the correct answer.

Question 4

If there are 13 heart cards in a deck of 52 cards,then what is the probability of selecting one heart card on a single draw from the deck of cards?

Accepted Answer

There are 13 heart cards in the deck of 52 cards. Therefore, the probability of selecting one heart card on a single draw from the deck of cards is 13/52, which can be simplified to 1/4.

Question 5

A researcher visits a population of 1,200 local residents to determine the proportion of local residents who support a new smoking ban.In this case,the sample space is

Accepted Answer

The sample space refers to the entire population from which a sample is taken. In this case, the population is the 1,200 local residents, therefore the sample space is equal to the total number (or population) of residents.

Question 6

A therapist goes through her records and finds that 200 of her 400 patients showed significant improvement in mental health over the past year.Hence,the probability of her patients showing significant improvement in mental health is

Accepted Answer

The probability is calculated by dividing the number of patients who showed significant improvement (200) by the total number of patients (400).

Probability = Number of successes/Total number of outcomes

Probability = 200/400
Probability = 0.5

Therefore, the probability of her patients showing significant improvement in mental health is 0.5 or 50%.

Question 7

The proportion or fraction of times an outcome is likely to occur is referred to as

Accepted Answer

Probability is defined as the proportion of times an outcome is likely to occur. Random events are events that occur by chance, but they do not necessarily have a specific probability. Sample space is the set of all possible outcomes of an experiment or event. Luck is often used to describe chance events that are perceived to be outside of our control.

Question 8

A researcher has participants choose between three advertisements.She finds that 54 prefer Ad A,86 prefer Ad B,and 60 prefer Ad C.The probability or proportion of participants preferring Ad B is

Accepted Answer

The probability or proportion of participants preferring Ad B is calculated by dividing the number of participants who chose Ad B by the total number of participants. Therefore, the proportion of participants preferring Ad B is 86/(54+86+60) = 0.43 or 43%. Therefore, the best choice is C.

Question 9

By definition,the probability of an outcome or event is

Accepted Answer

All of the options mentioned are correct. Probability is the measure of the likelihood of an event or outcome occurring. It can be expressed as a proportion or fraction of the total possible outcomes, and it is particularly useful in predicting the likelihood of random events.

Question 10

A researcher finds that 20 of 120 students failed an exam.In this case,the probability of failing this exam was

Accepted Answer

Probability is calculated by dividing the number of outcomes in an event by the total number of possible outcomes. In this case, the probability of failing the exam is given by 20/120, which simplifies to 1/6 or about .17 (rounded to two decimal places). Therefore, the best choice is B, which corresponds to .17.

Question 11

The following are six random outcomes for a sample space: -1,-3,-3,-2,-5,and -6.What is the probability of selecting a -3 in this example?

Accepted Answer

There are two -3's in the sample space out of a total of six outcomes, so the probability of selecting a -3 is 2/6 or 1/3. Therefore, the best choice is B, which represents this probability.

Question 12

A researcher records the following data for the number of bids made on a sample of items sold at an auction.Based on the table,what was the probability that an item had 7 bids made on it?

Accepted Answer

The answer of A researcher records the following data for...

Question 13

Which of the following is NOT a characteristic of probability?

Accepted Answer

Probability is used to describe random events, not fixed events.

Question 14

A researcher determines that the probability of winning a new game is p = .32.Assuming winning and losing are mutually exclusive events,what is the probability of winning and losing the new game?

Accepted Answer

Winning and losing are mutually exclusive events, meaning they cannot happen at the same time. Therefore, the probability of both winning and losing simultaneously is 0, making this outcome not possible.

Question 15

The probability that someone in the human population has blood type AB is about p = .08;the probability that someone has blood type O is about p = .25.Knowing that each individual can have one and only one blood type,what is the probability that a person has an AB or O blood type?

Accepted Answer

To find the probability that a person has an AB or O blood type, we can use the formula for the union of two events: P(AB or O) = P(AB) + P(O) - P(AB and O). However, since an individual can only have one blood type, the events AB and O are mutually exclusive (i.e. someone cannot have both blood types), so P(AB and O) = 0. Therefore, the formula simplifies to P(AB or O) = P(AB) + P(O) = 0.08 + 0.25 = 0.33. Thus, the correct answer is A.

Question 16

Probability allows us to make predictions regarding:

Accepted Answer

Probability allows us to make predictions regarding random events, outcomes, and variables. Therefore, all of the choices are correct.

Question 17

In a game,the probability of winning money is p = .16,the probability of losing money is p = .54,and the probability of breaking even is p = .30.What is the probability of winning or losing money in this game?

Accepted Answer

The probability of winning or losing money is the sum of the probabilities of winning and losing, which is .16+.54=.70. Therefore, the answer is C) .70.

Question 18

A news poll showed that voters had no preference for either of three candidates.In this example,the probability of a vote for,say,Candidate A equals

Accepted Answer

Since the news poll shows that voters have no preference for any of the three candidates, the probability of voting for any one of them would be equal. Since there are three candidates, the probability of a vote for Candidate A would be 1/3. Therefore, the answer is B) 1/3.

Question 19

The total number of possible outcomes for a random variable is referred to as

Accepted Answer

The sample space is the set of all possible outcomes for a random variable. The other answer choices are incorrect as probability refers to the likelihood of an outcome, a random event is a single outcome of a random experiment, and the sum is irrelevant to the total possible outcomes.

Question 20

A researcher determines the probability that a research study will reveal something new is p = .80.What is the probability that the study will reveal something new or not reveal something new?

Accepted Answer

The probability of revealing something new or not revealing something new is always 1 or 100%. Thus, the answer is C.

Quiz 5: Probability