Question 1

Once again using the example about supermarket fliers, we would have evidence that the "don't litter" message on the flier was effective if we found that
A) the probability of finding a flier with the message in the trash can was substantially higher than the probability calculated on the assumption that the two events were independent.
B) the probability of finding a flier with the message in the trash can was substantially lower than the probability calculated on the assumption that the two events were independent.
C) the probability of finding a flier with the message in the trash can was the same as the probability calculated on the assumption that the two events were independent.
D) We can't tell from the information available.

Accepted Answer

A

Question 2

To estimate that probability that the next vehicle to leave the parking lot will be a silver pickup, we first need to
A) assume that the color and the type of vehicle are mutually exclusive.
B) assume that the color and the type of vehicle are independent.
C) assume that the color and the type of vehicle are exhaustive.
D) simply multiply the two probabilities.

Accepted Answer

Assuming that the color and the type of vehicle are independent allows us to multiply the probabilities of each separately occurring, giving us the probability of the next vehicle being a silver pickup.

Question 3

A frequentistic approach to probability is likely to be invoked
A) in predicting the weather.
B) in calculating the chances of winning in craps.
C) in estimating the probability that a sharpshooter will score a bull's eye.
D) in blackjack.

Accepted Answer

C

Question 4

Using the example from the text about the supermarket fliers, when we calculate the probability that a flier will be left either among the canned goods or in the bottom of the shopping cart, we need to invoke
A) the additive rule.
B) the superlative rule.
C) the dependence rule.
D) the multiplicative rule.

Accepted Answer

The question is asking for the probability of two separate events happening (flier left among canned goods AND flier left in the bottom of the shopping cart), which means we need to use the additive rule of probability.

Question 5

Last year there were 300 new Ph.D.s in chemistry looking for academic jobs. Of those, 100 were women and 200 were men. Nationwide last year there were 75 new hirings in chemistry departments. How many of those new hires would be expected to be women if there was no gender discrimination?
A) 15
B) 20
C) 25
D) 50

Accepted Answer

If there was no gender discrimination, the expected number of hires for women would be proportional to their representation among the new Ph.D.s. Since 100 out of 300 new Ph.D.s were women, they represent 1/3 of the total. Therefore, if there were 75 new hirings, 1/3 of those, or 25, would be expected to be women.

Question 6

Out of a pool of 40 men and 10 women, all of whom are equally qualified for one position as an instructor in chemistry, the person hired was a male. The probability that this would happen if the department ignored gender as a variable in selection is
A) .40
B) .80
C) .50
D) .63

Accepted Answer

Since all candidates are equally qualified and there are four times as many men as women, the probability of selecting a male is 40/50 or 0.8.

Question 7

In the parking lot below me, 40% of the vehicles are silver, and about 25% of the vehicles are pickup trucks. The probability that the next vehicle to leave the parking lot will be a silver pickup is
A) .40
B) .65
C) .10
D) It can't be estimated without knowing that color and type of vehicle are independent.

Accepted Answer

The probability of a vehicle being both silver and a pickup truck depends on whether the characteristics of being silver and being a pickup truck are independent. Without knowing if the color and type of vehicle are independent variables, it's impossible to accurately calculate the probability of the next vehicle being a silver pickup truck.

Question 8

Two events are mutually exclusive when
A) the occurrence of one event is independent of the occurrence of the other.
B) the occurrence of one event precludes the occurrence of the other.
C) both events are equally likely.
D) the first event precedes the second event.

Accepted Answer

Mutually exclusive events cannot occur at the same time, so the occurrence of one event precludes the occurrence of the other. For example, flipping a coin and getting heads and tails are mutually exclusive events because getting one precludes getting the other.

Question 9

An exhaustive set of events is one which
A) we can never estimate.
B) contains all possible outcomes.
C) contains only independent events.
D) comes from running a very long series of sampling studies.

Accepted Answer

An exhaustive set of events must contain all possible outcomes, leaving no room for any other possibilities. It is necessary in certain probability and statistical analysis.

Question 10

I am looking down on a parking lot, and can see that about 10% of the cars are red and about 15% of the cars are blue. To estimate the probability that the next car to leave the lot will be red or blue, I would
A) add those two percentages.
B) multiply those two percentages.
C) count the number of green cars.
D) It can't be estimated from the information provided.

Accepted Answer

To estimate the probability of the next car being red or blue, we can simply add the percentage of red cars (10%) and the percentage of blue cars (15%), which gives us a rough estimate of 25%. Therefore, we choose option A.

Question 11

If I am interested in the probability that you will be depressed if you have experienced a great deal of stress in the past month, I am talking about
A) independence.
B) a joint probability.
C) a conditional probability.
D) an additive probability.

Accepted Answer

The question is asking about the probability of being depressed given that the person has experienced a great deal of stress in the past month, which is a conditional probability.

Question 12

If I am interested in the probability that you will be depressed and that you will have experienced a great deal of stress in the past month, I am talking about
A) independence.
B) a joint probability.
C) a conditional probability.
D) an additive probability.

Accepted Answer

A joint probability refers to the probability of two events happening at the same time. In this case, it's the probability of being depressed and having experienced a great deal of stress in the past month.

Question 13

When we want to calculate the probability of the joint occurrence of two or more independent events, we invoke
A) the multiplicative rule.
B) the additive rule.
C) the sum of independent probabilities.
D) Bernoulli's rule.

Accepted Answer

The multiplicative rule applies when we want to calculate the probability of the joint occurrence of two or more independent events. It states that the probability of the joint occurrence of two or more independent events is equal to the product of their individual probabilities.

Question 14

Using an example from the text, when we calculate the probability that a supermarket flier will be left among the canned goods if it contains a notice not to litter, we will be dealing with
A) the additive rule.
B) the superlative rule.
C) the dependence rule.
D) conditional probabilities.

Accepted Answer

We are dealing with conditional probabilities because the probability of finding the flier among the canned goods is dependent on the notice not to litter.

Question 15

Which of the following is NOT a way of setting probabilities?
A) the analytic view
B) the frequentistic view
C) the subjective view
D) the correlational view

Accepted Answer

The correlational view is not a recognized way of setting probabilities. The analytic view uses logical reasoning to determine probabilities, the frequentistic view uses observed frequencies to estimate probabilities, and the subjective view involves personal beliefs or expertise to assign probabilities.

Question 16

One difference between the additive and the multiplicative rules that helps us remember when to use which is
A) with the additive rule we are talking about the occurrence of one of several outcomes.
B) with the multiplicative rule we are talking about the occurrence of more than one kind of outcome.
C) the two rules are interchangeable.
D) both a and b

Accepted Answer

The additive rule is used when we are talking about the occurrence of one of several outcomes, while the multiplicative rule is used when we are talking about the occurrence of more than one kind of outcome. Therefore, both options A and B are correct, making choice D the best answer. The two rules are not interchangeable; they are used for different types of events.

Question 17

Where is "subjective probability" most likely to be invoked?
A) in setting the point spread in football
B) in deciding if tomorrow will be a good day
C) in calculating your best strategy in poker
D) in playing Russian roulette

Accepted Answer

Subjective probability refers to personal beliefs and judgments about the likelihood of an event occurring, rather than objective calculations based on statistical data. Predicting if tomorrow will be a good day is a subjective judgment that is likely based on personal experience and expectations, making it the most appropriate scenario for invoking subjective probability. The other options may involve objective calculations or rules.

Question 18

Which of the following is NOT an appropriate use of probability?
A) estimating the likelihood that a particular event will occur
B) calculating your chances of winning the lottery
C) placing bets at the track
D) knowing what event will happen next

Accepted Answer

Probability is used for estimating the likelihood or chance of an event occurring, but it cannot be used to determine exactly which event will happen next. The outcome of an event is not determined by the probability of it happening, but rather by the specific circumstances and factors involved.

Question 19

Of 50 women treated for breast cancer in the local cancer unit, 35 of them survived for at least 5 years. For a woman who has just been diagnosed with breast cancer, our best guess is that the probability that she will survive for 5 years is
A) 35/50 = .70
B) 15/35= .43
C) 35/100 = .35
D) we don't have enough information.

Accepted Answer

Out of the 50 women treated, 35 survived for at least 5 years. Therefore, the probability of survival for 5 years is 35/50, which simplifies to 0.70 or 70%.

Question 20

Following up on the preceding question, suppose that you found that 27 of the new hires were women. You would probably be justified in concluding that
A) there was discrimination against men.
B) there was discrimination against women.
C) there was no discrimination on the basis of gender.
D) we don't have enough information to even start to answer the question.

Accepted Answer

We cannot infer any discrimination based on this information alone. However, if additional information was given such as the percentage of women in the applicant pool or the qualifications of the new hires, we may be able to make a more informed judgement.

Quiz 7: Basic Concepts of Probability

Once again using the example about supermarket fliers, we would have evidence that the "don't litter" message on the flier was effective if we found that

To estimate that probability that the next vehicle to leave the parking lot will be a silver pickup, we first need to

A frequentistic approach to probability is likely to be invoked

Using the example from the text about the supermarket fliers, when we calculate the probability that a flier will be left either among the canned goods or in the bottom of the shopping cart, we need to invoke

Last year there were 300 new Ph.D.s in chemistry looking for academic jobs. Of those, 100 were women and 200 were men. Nationwide last year there were 75 new hirings in chemistry departments. How many of those new hires would be expected to be women if there was no gender discrimination?

Out of a pool of 40 men and 10 women, all of whom are equally qualified for one position as an instructor in chemistry, the person hired was a male. The probability that this would happen if the department ignored gender as a variable in selection is

In the parking lot below me, 40% of the vehicles are silver, and about 25% of the vehicles are pickup trucks. The probability that the next vehicle to leave the parking lot will be a silver pickup is

Two events are mutually exclusive when

An exhaustive set of events is one which

I am looking down on a parking lot, and can see that about 10% of the cars are red and about 15% of the cars are blue. To estimate the probability that the next car to leave the lot will be red or blue, I would

If I am interested in the probability that you will be depressed if you have experienced a great deal of stress in the past month, I am talking about

If I am interested in the probability that you will be depressed and that you will have experienced a great deal of stress in the past month, I am talking about

When we want to calculate the probability of the joint occurrence of two or more independent events, we invoke

Using an example from the text, when we calculate the probability that a supermarket flier will be left among the canned goods if it contains a notice not to litter, we will be dealing with

Which of the following is NOT a way of setting probabilities?

One difference between the additive and the multiplicative rules that helps us remember when to use which is

Where is "subjective probability" most likely to be invoked?

Which of the following is NOT an appropriate use of probability?

Of 50 women treated for breast cancer in the local cancer unit, 35 of them survived for at least 5 years. For a woman who has just been diagnosed with breast cancer, our best guess is that the probability that she will survive for 5 years is

Following up on the preceding question, suppose that you found that 27 of the new hires were women. You would probably be justified in concluding that