Question 1

If A and B,are independent events, then P(A) = P(B A ).

Accepted Answer

For independent events A and B, P(B|A) = P(B), not P(A) = P(B|A).

Question 2

You need to fly from Dallas to Chicago. Five airlines offer direct flights, and each airline offers 4 direct flights on the day you need to travel. How many ways can you choose a direct flight from Dallas to Chicago?.

Accepted Answer

The answer of You need to fly from Dallas to...

Question 3

A popular restaurant occasionally offers a three-course meal for a fixed price. The customer chooses one appetizer, one entree, and one dessert from a special menu. There are four choices for the appetizer, five choices for the entree, and three choices for the dessert. How many different ways can a customer choose the three courses?

Accepted Answer

The answer of A popular restaurant occasionally offers a three-course...

Question 4

$$\mathrm { P } _ { 4 } ^ { 5 }$$

Accepted Answer

The answer of \[\mathrm { P } _ { 4...

Question 5

Determine the number of sample points in the sample space corresponding to the experiment of tossing two coins and one die.

Accepted Answer

The answer of Determine the number of sample points in...

Question 6

Classify the events as dependent or independent: Events A and B where P(A) = 0.6, P(B) = 0.8, and P(A and B) = 0.47.

Accepted Answer

The events are dependent because P(A and B) ≠ P(A) * P(B). Here, 0.47 ≠ 0.6 * 0.8 (which equals 0.48).

Question 7

A basketball player has an 80% chance of making the first free-throw he shoots. If he makes the first free-throw shot, then he has a 90% chance of making the second free-throw he shoots. If he misses the first free-throw shot, then he only has a 70% chance of making the second free-throw he shoots. Suppose this player has been awarded two free-throw shots. Are the events, A - the player makes the first shot, and B - the player makes the second shot, independent events?

Accepted Answer

The probability of making the second shot depends on whether the first shot was made or not. Therefore, the events are not independent.

Question 8

A rental company offers 12 choices of table linens, three choices of china, two choices of flatware, and three choices of stemware. In how many ways can a customer choose one of each to set the tables for a wedding reception?

Accepted Answer

The total number of ways to choose one of each item is the product of the number of choices for each category: 12 (linens) * 3 (china) * 2 (flatware) * 3 (stemware) = 216.

Question 9

If A and B are independent events, then A and B are also mutually exclusive.

Accepted Answer

If A and B are independent, it means that the occurrence of A does not affect the probability of B and vice versa. However, if A and B are mutually exclusive, it means that they cannot occur at the same time. Therefore, the statement is false as independent events can still occur simultaneously.

Question 10

Suppose two dice, one blue and one red, are rolled and the outcomes of each are recorded. We define the following two events: A: sum of the roll is 7 B. the result of the blue die is a number greater than 4 Are the two events, A and B, independent events?

Accepted Answer

The answer of Suppose two dice, one blue and one...

Question 11

Two events, A and B, are independent if $$P ( A \text { and } B ) = P ( A ) \times P ( B ) \text {. }$$

Accepted Answer

Two events A and B are independent if the probability of both events occurring together is equal to the product of their individual probabilities.

Question 12

Five people have collaborated on a new television show. Because they all have big egos, they each want their names listed first in the credits for the new show. How many different ways can the names be ordered if they are randomly listed?

Accepted Answer

The number of ways to order 5 names is given by 5! (5 factorial), which is 5 x 4 x 3 x 2 x 1 = 120.

Question 13

In BIG GAME, you must select six numbers from fifty-two numbers to win the big prize. The numbers do not have to be in a particular order. What is the probability that any particular six-digit combination will be chosen?

Accepted Answer

The answer of In BIG GAME, you must select six...

Question 14

Determine the number of sample points in the sample space corresponding to the experiment of tossing 3 dice.

Accepted Answer

Each die has 6 faces, so for 3 dice, the total number of outcomes is 6 * 6 * 6 = 216.

Question 15

Determine the number of sample points in the sample space corresponding to the experiment of tossing a coin 6 times.

Accepted Answer

Each coin toss has 2 possible outcomes (heads or tails). Therefore, for 6 tosses, the total number of sample points is 2^6 = 64.

Question 16

To win at BIG GAME in a certain state, one must correctly select 6 numbers from a collection of 52 numbers (1 through 52). The order in which the selections is made does not matter. How many different 6 -number selections are possible, assuming no repetition of numbers?

Accepted Answer

The number of different 6-number selections is given by the combination formula:C(52, 6) = 52! / (6! * (52-6)!) = 20,361,111

Question 17

A financial advisor has recommended three high-risk high-yield investments and four low-risk low-yield investments to one of her clients. In how many ways can the client select one of each type of investment for his portfolio?

Accepted Answer

The client can choose one high-risk investment in 3 ways and one low-risk investment in 4 ways. Therefore, the total number of ways to select one of each type is 3 * 4 = 12.

Question 18

A statistics quiz has 5 multiple choice questions with four answer choices each and 5 true/false questions. How many different ways can a student answer the questions by guessing?

Accepted Answer

The answer of A statistics quiz has 5 multiple choice...

Question 19

Which of the following best characterizes a random sample?

Accepted Answer

A random sample is characterized by every set of n elements in the population having an equal probability of being chosen, ensuring that the sample is representative of the population.

Question 20

From 8 names on a list, a sample of 3 will be asked about voting preferences in an upcoming election. How many different samples are possible?

Accepted Answer

The number of different samples is calculated using combinations, not permutations, because the order of selection does not matter. The formula for combinations is C(n, r) = n! / (r!(n-r)!), where n is the total number of items to choose from, and r is the number of items to choose. Here, C(8, 3) = 8! / (3!(8-3)!) = 56.

Quiz 3: Probability

If A and B,are independent events, then P(A) = P(B A ).

You need to fly from Dallas to Chicago. Five airlines offer direct flights, and each airline offers 4 direct flights on the day you need to travel. How many ways can you choose a direct flight from Dallas to Chicago?.

$\mathrm { P } _ { 4 } ^ { 5 }$

Determine the number of sample points in the sample space corresponding to the experiment of tossing two coins and one die.

Classify the events as dependent or independent: Events A and B where P(A) = 0.6, P(B) = 0.8, and P(A and B) = 0.47.

A rental company offers 12 choices of table linens, three choices of china, two choices of flatware, and three choices of stemware. In how many ways can a customer choose one of each to set the tables for a wedding reception?

If A and B are independent events, then A and B are also mutually exclusive.

Suppose two dice, one blue and one red, are rolled and the outcomes of each are recorded. We define the following two events: A: sum of the roll is 7 B. the result of the blue die is a number greater than 4 Are the two events, A and B, independent events?

Two events, A and B, are independent if $P ( A \text { and } B ) = P ( A ) \times P ( B ) \text {. }$

Five people have collaborated on a new television show. Because they all have big egos, they each want their names listed first in the credits for the new show. How many different ways can the names be ordered if they are randomly listed?

In BIG GAME, you must select six numbers from fifty-two numbers to win the big prize. The numbers do not have to be in a particular order. What is the probability that any particular six-digit combination will be chosen?

Determine the number of sample points in the sample space corresponding to the experiment of tossing 3 dice.

Determine the number of sample points in the sample space corresponding to the experiment of tossing a coin 6 times.

To win at BIG GAME in a certain state, one must correctly select 6 numbers from a collection of 52 numbers (1 through 52) . The order in which the selections is made does not matter. How many different 6 -number selections are possible, assuming no repetition of numbers?

A financial advisor has recommended three high-risk high-yield investments and four low-risk low-yield investments to one of her clients. In how many ways can the client select one of each type of investment for his portfolio?

A statistics quiz has 5 multiple choice questions with four answer choices each and 5 true/false questions. How many different ways can a student answer the questions by guessing?

Which of the following best characterizes a random sample?

From 8 names on a list, a sample of 3 will be asked about voting preferences in an upcoming election. How many different samples are possible?

Quiz 3: Probability

If A and B,are independent events, then P(A) = P(B A ).

You need to fly from Dallas to Chicago. Five airlines offer direct flights, and each airline offers 4 direct flights on the day you need to travel. How many ways can you choose a direct flight from Dallas to Chicago?.

P45\mathrm { P } _ { 4 } ^ { 5 }P45​

Determine the number of sample points in the sample space corresponding to the experiment of tossing two coins and one die.

Classify the events as dependent or independent: Events A and B where P(A) = 0.6, P(B) = 0.8, and P(A and B) = 0.47.

A rental company offers 12 choices of table linens, three choices of china, two choices of flatware, and three choices of stemware. In how many ways can a customer choose one of each to set the tables for a wedding reception?

If A and B are independent events, then A and B are also mutually exclusive.

Suppose two dice, one blue and one red, are rolled and the outcomes of each are recorded. We define the following two events: A: sum of the roll is 7 B. the result of the blue die is a number greater than 4 Are the two events, A and B, independent events?

Two events, A and B, are independent if P(A and B)=P(A)×P(B). P ( A \text { and } B ) = P ( A ) \times P ( B ) \text {. }P(A and B)=P(A)×P(B).

Five people have collaborated on a new television show. Because they all have big egos, they each want their names listed first in the credits for the new show. How many different ways can the names be ordered if they are randomly listed?

In BIG GAME, you must select six numbers from fifty-two numbers to win the big prize. The numbers do not have to be in a particular order. What is the probability that any particular six-digit combination will be chosen?

Determine the number of sample points in the sample space corresponding to the experiment of tossing 3 dice.

Determine the number of sample points in the sample space corresponding to the experiment of tossing a coin 6 times.

To win at BIG GAME in a certain state, one must correctly select 6 numbers from a collection of 52 numbers (1 through 52) . The order in which the selections is made does not matter. How many different 6 -number selections are possible, assuming no repetition of numbers?

A financial advisor has recommended three high-risk high-yield investments and four low-risk low-yield investments to one of her clients. In how many ways can the client select one of each type of investment for his portfolio?

A statistics quiz has 5 multiple choice questions with four answer choices each and 5 true/false questions. How many different ways can a student answer the questions by guessing?

Which of the following best characterizes a random sample?

From 8 names on a list, a sample of 3 will be asked about voting preferences in an upcoming election. How many different samples are possible?

$\mathrm { P } _ { 4 } ^ { 5 }$

Two events, A and B, are independent if $P ( A \text { and } B ) = P ( A ) \times P ( B ) \text {. }$