Question 1

Of the delegates at a convention, 60% attended the breakfast forum, 70% attended the dinner speech, and 40% attended both events.
a. If a randomly selected delegate is known to have attended the dinner speech, what is the probability he or she also attended the breakfast forum?
______________
b. What is the probability that a randomly selected delegate either attended the breakfast forum, or attended the dinner speech, or attended both?
______________

Accepted Answer

The answer of Of the delegates at a convention, 60%...

Question 2

Applicants for a musical instrument manufacturer are asked to take a manual dexterity test. Past history has shown that only 25% of the applicants are able to finish the test in the allotted time. Two applicants are selected at random from the applicant pool.
a. What is the probability that both applicants finish the test in the allotted time?
________________________________________________________
b. Justify your answer.
______________
c. What is the probability the first applicant completes the test in the allotted time but the second applicant does not?
______________
d. Justify your answer.
________________________________________________________

Accepted Answer

The answer of Applicants for a musical instrument manufacturer are...

Question 3

A box contains one red, three blue and two green marbles. Two marbles are randomly selected without replacement. Let
R = {The selected marble is red.}
B = {The selected marble is blue.}
G = {The selected marble is green.}
C = {Both marbles selected are the same color.}
D = {At least one of the marbles is blue.}
a. Find P(C).
______________
b. Find P(D).
______________
c. Find
  .
______________ 
d. Find
  .
______________ 
e. Find P(D | C).
______________

Accepted Answer

The answer of A box contains one red, three blue...

Question 4

Four different kinds of radar systems, designed to detect or monitor the airspace around a major airport for high flying objects, low flying objects, runway traffic, and wind shear, operate independently. If each system has probability 0.90 of functioning correctly, find the probability at least one radar system will fail.
______________

Accepted Answer

The answer of Four different kinds of radar systems, designed...

Question 5

Relative frequency histograms are constructed for a sample of n measurements drawn from the population, while the probability histogram is constructed as a model for the entire population of measurements.

Accepted Answer

Relative frequency histograms represent the distribution of data in a sample by showing the proportion of observations within each category or interval, whereas probability histograms model the theoretical distribution of data for an entire population, indicating the probability of observations falling within each category or interval.

Question 6

The probability of an event A is equal to the sum of the probabilities of the simple events contained in A.

Accepted Answer

This is one of the basic axioms of probability theory known as the additivity rule.

Question 7

Suppose that P(A) = 0.4, P(B) = 0.5, and that events A and B are mutually exclusive.
a. Find
  .
______________ 
b. Find
  .
______________

Accepted Answer

The answer of Suppose that P(A) = 0.4, P(B) =...

Question 8

A university in Alabama has 1000 employees. Four hundred of the employees have at least 20 years of experience (event A), 100 are African American (event B), and 300 with a background in Microsoft Office 2003 (event C). Assume events A, B, and C are independent.
a. What is the probability of finding an employee who meets all three of these criteria?
______________
b. What is the probability of finding an employee who meets at least two of the three criteria?
______________

Accepted Answer

The answer of A university in Alabama has 1000 employees....

Question 9

A student has decided to study at a local coffee shop. After some time, she gets hungry. There are two beverages available: tea and coffee and three bakery items: donuts, muffins and bagels. Define the following events:
C = {student gets coffee to drink}
T = {student gets tea to drink}
D = {student gets a donut to eat}
M = {student gets a muffin to eat}
B = {student gets a bagel to eat}
a. She decides she wants to get one item to eat and one item to drink. List the elements in the sample space S.
____________________________
b. If each combination is equally likely, what is the probability the student gets coffee and a bagel?
______________
c. If each combination is equally likely, what is the probability the student gets a muffin and coffee or tea?
______________
d. If each combination is equally likely, what is the probability the student does not get a donut?
______________

Accepted Answer

The answer of A student has decided to study at...

Question 10

A federal agency is trying to decide which of two waste management projects to investigate as the source of air pollution. In the past, projects of the first type were in violation of air quality standards with probability 0.3 on any given day, while projects of the second type were in violation of air quality standards with probability 0.25 on any given day. It is not possible for both projects to pollute the air in one day. Let A_i, i = 1, 2, denote that project of type i was in violation of air quality standards. a. Find the probability of an air pollution problem caused by either the first project or the second project. ______________ b. If the first project is violating air quality standards, what is the probability the second project is also violating federal air quality standards? ______________

Accepted Answer

The answer of A federal agency is trying to decide...

Question 11

At a local pet adoption center for dogs and cats, it is known that if a person adopts a pet, there is a 0.45 probability that it will be a cat and a 0.55 probability that it will be a dog. If a cat is adopted, the probability that it is female is 0.60. If a dog is adopted, the probability that it is female is 0.35. An adopted pet is selected at random and is found to be male. What is the probability that the adopted pet is a dog?
______________

Accepted Answer

The answer of At a local pet adoption center for...

Question 12

Combinations are distinguishable ordered arrangements of items all of which have been drawn from a given group of items.

Accepted Answer

Combinations refer to the selection of items from a group where the order does not matter, unlike permutations where the order is important.

Question 13

Probability is the tool that allows the statistician to use sample information to make inferences about or describe the population from which the sample was drawn.

Accepted Answer

This statement is true. Probability calculations allow statisticians to make conclusions or predictions about the larger population based on the sample data they have collected.

Question 14

Lily frequents one of two fast food restaurants, choosing McDonald 25% of the time and Burger King 75% of the time. Regardless of where she goes, she buys French Fries on 60% of her visits.
a. The next time Lily goes into a fast food restaurant, what is the probability that she goes to McDonald and orders a French Fries?
______________
b. Are the two events in the previous question independent? Explain.
______________
c. Explain.
________________________________________________________
d. If Lily goes to a fast food restaurant and orders French Fries, what is the probability that she is at Burger King?
______________
e. What is the probability that Lily goes to McDonald, or orders French Fries, or both?
______________

Accepted Answer

The answer of Lily frequents one of two fast food...

Question 15

A hand soap manufacturer introduced a new liquid, lotion-enriched, antibacterial soap and conducted an extensive consumer survey to help judge the success of the new product. The survey showed 40% of the consumers had seen an advertisement for the new soap, 20% had tried the new soap, and 15% had both seen an advertisement and tried the new soap. Let event A denote that the consumers had seen an ad for the new soap, and event B denote that the consumers had tried the new soap.
a. What is the probability a randomly selected consumer had either seen an advertisement or tried the new soap?
______________
b. If a randomly chosen consumer has seen an advertisement for the new soap, what is the probability he or she has tried the product?
______________

Accepted Answer

The answer of A hand soap manufacturer introduced a new...

Question 16

An experiment consists of tossing 4 unbiased coins simultaneously. The number of simple events in this experiment is 16.

Accepted Answer

Each coin has 2 possible outcomes (heads or tails), so for 4 coins, the total number of simple events is 2^4 = 16.

Question 17

A laboratory test for a disease affecting 5% of the population is either positive, indicating the disease is present, or negative, indicating the disease is not present. When people having the disease are tested, 80% of the tests come back positive, and when people who don't have the disease are tested, 15% of the tests come back from the lab marked positive (a false positive result). What is the chance a randomly chosen person's test results would come back positive?
______________

Accepted Answer

The answer of A laboratory test for a disease affecting...

Question 18

Statistics reasons from the population to the sample, whereas probability acts in reverse, moving from the sample to the population.

Accepted Answer

Statistics involves studying a sample in order to make inferences about the population from which it was drawn, while probability involves using information about a sample to make predictions about the likelihood or distribution of certain outcomes in the population. Therefore, statistics moves from the population to the sample, while probability operates in the opposite direction.

Question 19

An experiment is any activity that results in one and only one of several clearly defined possible outcomes but that does not allow us to tell in advance which of these will prevail in any particular instance.

Accepted Answer

This statement accurately describes what an experiment is. It involves a series of trials or events that could have different outcomes, but the exact result cannot be predicted in any given instance.

Question 20

Suppose that P(A) = 0.6, P(B) = 0.7, and that events A and B are independent.
a. Find
  .
______________ 
b. Find
  .
______________ 
c. Find P (A / B).
______________
d. Find P (B / A).
______________

Accepted Answer

The answer of Suppose that P(A) = 0.6, P(B) =...

Quiz 4: Probability and Probability Distributions

Relative frequency histograms are constructed for a sample of n measurements drawn from the population, while the probability histogram is constructed as a model for the entire population of measurements.

The probability of an event A is equal to the sum of the probabilities of the simple events contained in A.

Suppose that P(A) = 0.4, P(B) = 0.5, and that events A and B are mutually exclusive. a. Find . b. Find .

Combinations are distinguishable ordered arrangements of items all of which have been drawn from a given group of items.

Probability is the tool that allows the statistician to use sample information to make inferences about or describe the population from which the sample was drawn.

An experiment consists of tossing 4 unbiased coins simultaneously. The number of simple events in this experiment is 16.

Statistics reasons from the population to the sample, whereas probability acts in reverse, moving from the sample to the population.

An experiment is any activity that results in one and only one of several clearly defined possible outcomes but that does not allow us to tell in advance which of these will prevail in any particular instance.

Suppose that P(A) = 0.6, P(B) = 0.7, and that events A and B are independent. a. Find . b. Find . c. Find P (A / B). d. Find P (B / A).

Quiz 4: Probability and Probability Distributions

Relative frequency histograms are constructed for a sample of n measurements drawn from the population, while the probability histogram is constructed as a model for the entire population of measurements.

The probability of an event A is equal to the sum of the probabilities of the simple events contained in A.

Suppose that P(A) = 0.4, P(B) = 0.5, and that events A and B are mutually exclusive. a. Find . ______________ b. Find . ______________

Combinations are distinguishable ordered arrangements of items all of which have been drawn from a given group of items.

Probability is the tool that allows the statistician to use sample information to make inferences about or describe the population from which the sample was drawn.

An experiment consists of tossing 4 unbiased coins simultaneously. The number of simple events in this experiment is 16.

Statistics reasons from the population to the sample, whereas probability acts in reverse, moving from the sample to the population.

An experiment is any activity that results in one and only one of several clearly defined possible outcomes but that does not allow us to tell in advance which of these will prevail in any particular instance.

Suppose that P(A) = 0.6, P(B) = 0.7, and that events A and B are independent. a. Find . ______________ b. Find . ______________ c. Find P (A / B). ______________ d. Find P (B / A). ______________

Suppose that P(A) = 0.4, P(B) = 0.5, and that events A and B are mutually exclusive. a. Find . b. Find .

Suppose that P(A) = 0.6, P(B) = 0.7, and that events A and B are independent. a. Find . b. Find . c. Find P (A / B). d. Find P (B / A).