Question 1

S = {E1, E2, E3, E4, E5, E6}.A = {E1, E4}.What is A′?

Accepted Answer

A′ represents the complement of A with respect to S, which includes all elements in S that are not in A. Since A = {E1, E4}, A′ = {E2, E3, E5, E6}.

Question 2

For any two events A and B, if A∩B = { } (where { } is defined as the empty set), then A and B are said to be:

Accepted Answer

Disjoint events are events that have no outcomes in common. Therefore, if A∩B = { }, A and B are disjoint events.

Question 3

For any two events denoted A and B, the event A∩B is best described as:

Accepted Answer

A∩B represents the intersection of events A and B, which includes only outcomes that belong to both A and B.

Question 4

Sixty-five percent of the students who take introductory statistics start the semester with a poor opinion of statistics.If a randomly selected introductory statistics student has a poor opinion of statistics at the beginning of the semester, what is the probability that the person has had some negative experience with a previous math class?

Accepted Answer

Although the problem does not provide the conditional probability directly, we can use Bayes' theorem to calculate it. Let A be the event that the student has had a negative experience with a previous math class and B be the event that the student has a poor opinion of statistics at the beginning of the semester. Then, we want to find P(A|B).
From the problem, we know that P(B|A) = 0.80 (i.e., if a student has had a negative experience with a previous math class, there is an 80% chance that they have a poor opinion of statistics at the beginning of the semester). Also, P(B|A') = 0.60 (i.e., if a student has not had a negative experience with a previous math class, there is a 60% chance that they have a poor opinion of statistics at the beginning of the semester). 
We need to calculate P(A), which is not provided in the problem. However, we can make an assumption that P(A) = 0.50 (i.e., 50% of the students have had a negative experience with a previous math class). 
Using Bayes' theorem, we have:
P(A|B) = P(B|A)P(A) / [P(B|A)P(A) + P(B|A')(1-P(A))]
= 0.80 * 0.50 / [0.80*0.50 + 0.60*0.50]
= 0.6923
Therefore, the probability that a student with a poor opinion of statistics has had some negative experience with a previous math class is 0.6923, or approximately 69.23%. 
So, the best choice is C.

Question 5

Suppose we have a group of 5 children and wish to randomly select 2 from the group without replacement.How many possible unique samples of size 2 are possible if the order of selection does not matter?

Accepted Answer

The number of possible unique samples of size 2 without replacement can be calculated using the combination formula: C(5,2) = 5!/[2!(5-2)!] = 10. Therefore, the answer is D) 10.

Question 6

A recent demographic study conducted in the U.S.South classified all surveyed participants into one of only five possible religious categories: Roman Catholic, Protestant, Islamic, Jewish, Other.The table summarizes the survey results. ​  ​
Find P(Roman Catholic′).

Accepted Answer

The answer of A recent demographic study conducted in the...

Question 7

Suppose you roll a pair of dice.What is the probability that you roll the two dice so that they add up to 7 or 11?

Accepted Answer

There are 36 possible outcomes when rolling a pair of dice (6 possible outcomes for the first die multiplied by 6 possible outcomes for the second die). To find the probability of rolling a sum of 7 or 11, we count the possible outcomes that add up to 7 or 11 and divide by the total number of possible outcomes. 
For a sum of 7, there are 6 possible outcomes: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). 
For a sum of 11, there are 2 possible outcomes: (5,6) and (6,5). 
Therefore, the total number of possible outcomes is 6 + 2 = 8, and the probability is 8/36, which reduces to 2/9 or approximately 0.22. 
Thus, the best choice is C, 8/36.

Question 8

Which of the following is equal to  ?

Accepted Answer

The last part of the hexadecimal number (1dd9acd1e4bc) is a unique identifier and therefore cannot be altered. The only difference between the given number and the options is the fourth digit in the third block (03fe should be 03ff). Therefore, option A is the correct answer.

Question 9

A tree diagram is:

Accepted Answer

A tree diagram is a visual tool that is commonly used in probability theory to depict the possible outcomes of an event. In particular, it is used to graphically depict a sample space, or the set of all possible outcomes of an experiment. This type of diagram is helpful because it clearly delineates the potential outcomes and allows for easy calculation of probabilities. While it is an important tool, it is not the only method for determining accurate probability estimates.

Question 10

0! =

Accepted Answer

The factorial of 0 is defined as 1.

Question 11

Three factory workers work independently assembling office chairs for a local furniture wholesaler.Each worker completely assembles one chair per day.Worker number 1 has a defect rate of 0.01, worker number 2 has a defect rate of 0.15, and worker number 3 has a defect rate of 0.19 (workers 2 and 3 are very poor workers).What is the probability that on any given day, the workers produce three defective chairs?

Accepted Answer

The probability that all three workers produce defective chairs on any given day is the product of their individual defect rates: 0.01 * 0.15 * 0.19 = 2.85 × 10^-4.

Question 12

How many two-digit numbers are there, with both digits odd?

Accepted Answer

For a two-digit number with both digits odd, the first digit can be any odd number from 1 to 9, and the second digit can also be any odd number from 1 to 9. Therefore, there are 5 options for each digit (1, 3, 5, 7, or 9), resulting in a total of 5 x 5 = 25 possible two-digit numbers with both digits odd.

Question 13

If { } is defined as the empty set, then by definition P({ }) must be:

Accepted Answer

The power set of the empty set is a set of all subsets of the empty set. Since there are no elements in the empty set, there are no subsets of it, so P({ }) = { { } }, which is a set containing only the empty set. Therefore, P({ }) is equal to 1, not 0.

Question 14

If the outcome of one event has no bearing on the probability of another, the two events are said to be:

Accepted Answer

If two events are independent, the outcome of one event has no effect on the probability of the other event occurring.

Question 15

Steve has 18 black socks and 12 blue socks.Every morning he pulls a sock at random from his drawer, then pulls a second sock at random, and wears both socks, regardless of their color.What is the probability he wears mismatched socks?

Accepted Answer

The answer of Steve has 18 black socks and 12...

Question 16

Suppose a population contains 1,000,000 people, 5000 of whom have a disease.The table shows the number of people who have the disease and test positive, etc. ​  ​
Based on the table, what is the probability that a person who tests positive actually has the disease?

Accepted Answer

The answer of Suppose a population contains 1,000,000 people, 5000...

Question 17

The California Lottery's Super Lotto Plus game involves picking five numbers between 1 and 47.There are 1,533,939 different ways that five numbers could be picked, and 571,341 different ways to pick at least one pair of consecutive numbers in this lottery game.What is the probability a person playing this game picks at least one pair of consecutive numbers?

Accepted Answer

The probability of picking at least one pair of consecutive numbers is calculated by dividing the number of ways to pick at least one pair of consecutive numbers (571,341) by the total number of ways to pick five numbers (1,533,939). This gives a probability of 0.3725.

Question 18

An experiment consists of three tosses of a two-sided coin with the possible outcomes heads (H) or tails (T) from each toss.The outcome space is: ​
S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
​
We define event A as "no heads are observed" and event B as "no tails are observed." What is AUB?

Accepted Answer

AUB represents the union of events A and B. Event A is "no heads are observed," which corresponds to {TTT}. Event B is "no tails are observed," which corresponds to {HHH}. The union of these two events is {TTT, HHH}.

Question 19

A wildlife biology crew is tagging deer in California for a census.If, on a statewide basis, 40% of deer are males (bucks), what is the probability that the crew will randomly and independently tag three females (does) in a row, assuming the area's deer population is representative of the entire state? (Assume an infinite population.)

Accepted Answer

The probability of tagging a female deer is 60% (100% - 40%). Since the events are independent, the probability of tagging three females in a row is 0.6 * 0.6 * 0.6 = 0.216.

Question 20

The current form of the Milton Bradley board game Life includes a circular spinner that has 10 evenly spaced numbers around the edge, which specify the number of places a character will move.Assuming the spinner is balanced, the outcomes 1 through 10 inclusive are equally likely.On your next turn, you must move more than 4 spaces to be in the lead.However, in your current location on the game board, every other space (each odd space) gives you an undesirable result.What is the probability that on your next turn you will be in the lead and not have an undesirable result?

Accepted Answer

To be in the lead, we need to move 5 or more spaces. The only way we can have an undesirable result is if we land on an odd space during that move. So, we need to calculate the probability of getting a 5, 6, 7, 8, 9 or 10 on the spinner and not landing on an odd space. 
There are 6 numbers that satisfy this: 5, 6, 7, 8, 9, and 10. The probability of any of them arising is 1/6. However, the probability of not landing on an odd space is 1/2. Therefore, the probability of both events occurring is (1/6) * (1/2) = 1/12. 
Since we need to get a 5 or higher and not land on an odd space, we can add up the probabilities of getting a 5 or higher and subtract the probabilities of landing on an odd space for each of these outcomes:
P(5 or 6) = 1/6 + 1/2 = 2/3
P(7 or 8) = 1/6 + 1/2 = 2/3
P(9 or 10) = 1/6 + 1/2 = 2/3
Therefore, the probability of being in the lead and not having an undesirable result is:
(2/3 + 2/3 + 2/3) / 6 = 6/18 = 1/3 = 0.3.

So the answer is (C) 0.3.

Quiz 5: Probability

S = {E1, E2, E3, E4, E5, E6}.A = {E1, E4}.What is A′?

For any two events A and B, if A∩B = { } (where { } is defined as the empty set) , then A and B are said to be:

For any two events denoted A and B, the event A∩B is best described as:

Suppose we have a group of 5 children and wish to randomly select 2 from the group without replacement.How many possible unique samples of size 2 are possible if the order of selection does not matter?

A recent demographic study conducted in the U.S.South classified all surveyed participants into one of only five possible religious categories: Roman Catholic, Protestant, Islamic, Jewish, Other.The table summarizes the survey results. Find P(Roman Catholic′) .

Suppose you roll a pair of dice.What is the probability that you roll the two dice so that they add up to 7 or 11?

Which of the following is equal to ?

A tree diagram is:

0! =

How many two-digit numbers are there, with both digits odd?

If { } is defined as the empty set, then by definition P({ }) must be:

If the outcome of one event has no bearing on the probability of another, the two events are said to be:

Steve has 18 black socks and 12 blue socks.Every morning he pulls a sock at random from his drawer, then pulls a second sock at random, and wears both socks, regardless of their color.What is the probability he wears mismatched socks?

Suppose a population contains 1,000,000 people, 5000 of whom have a disease.The table shows the number of people who have the disease and test positive, etc. Based on the table, what is the probability that a person who tests positive actually has the disease?

An experiment consists of three tosses of a two-sided coin with the possible outcomes heads (H) or tails (T) from each toss.The outcome space is: S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} We define event A as "no heads are observed" and event B as "no tails are observed." What is AUB?

Quiz 5: Probability

S = {E1, E2, E3, E4, E5, E6}.A = {E1, E4}.What is A′?

For any two events A and B, if A∩B = { } (where { } is defined as the empty set) , then A and B are said to be:

For any two events denoted A and B, the event A∩B is best described as:

Suppose we have a group of 5 children and wish to randomly select 2 from the group without replacement.How many possible unique samples of size 2 are possible if the order of selection does not matter?

A recent demographic study conducted in the U.S.South classified all surveyed participants into one of only five possible religious categories: Roman Catholic, Protestant, Islamic, Jewish, Other.The table summarizes the survey results. ​ ​ Find P(Roman Catholic′) .

Suppose you roll a pair of dice.What is the probability that you roll the two dice so that they add up to 7 or 11?

Which of the following is equal to ?

A tree diagram is:

0! =

How many two-digit numbers are there, with both digits odd?

If { } is defined as the empty set, then by definition P({ }) must be:

If the outcome of one event has no bearing on the probability of another, the two events are said to be:

Steve has 18 black socks and 12 blue socks.Every morning he pulls a sock at random from his drawer, then pulls a second sock at random, and wears both socks, regardless of their color.What is the probability he wears mismatched socks?

Suppose a population contains 1,000,000 people, 5000 of whom have a disease.The table shows the number of people who have the disease and test positive, etc. ​ ​ Based on the table, what is the probability that a person who tests positive actually has the disease?

An experiment consists of three tosses of a two-sided coin with the possible outcomes heads (H) or tails (T) from each toss.The outcome space is: ​ S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} ​ We define event A as "no heads are observed" and event B as "no tails are observed." What is AUB?

A recent demographic study conducted in the U.S.South classified all surveyed participants into one of only five possible religious categories: Roman Catholic, Protestant, Islamic, Jewish, Other.The table summarizes the survey results. Find P(Roman Catholic′) .

Suppose a population contains 1,000,000 people, 5000 of whom have a disease.The table shows the number of people who have the disease and test positive, etc. Based on the table, what is the probability that a person who tests positive actually has the disease?

An experiment consists of three tosses of a two-sided coin with the possible outcomes heads (H) or tails (T) from each toss.The outcome space is: S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} We define event A as "no heads are observed" and event B as "no tails are observed." What is AUB?