Question 1

In a box of 50 markers, 30 markers are either red or black, 20 are missing their caps, and 12
markers are either red or black and are missing their caps. Are the events ʺred or blackʺ
and ʺmissing capʺ dependent or independent? Explain.

Accepted Answer

The answer of In a box of 50 markers, 30...

Question 2

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 outcome of the blue die does not affect the sum of the roll, and vice versa. Therefore, the events A and B are independent.

Question 3

Classify the events as dependent or independent: Events A and B where P(A)= 0.9, P(B)= 0.1, and P(A andB)= 0.09.

Accepted Answer

Events A and B are independent because the probability of A and B occurring together (P(A and B) = 0.09) is equal to the product of their individual probabilities (P(A) * P(B) = 0.9 * 0.1 = 0.09).

Question 4

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 missed, indicating that events A and B are not independent.

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

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

Accepted Answer

Each toss of a coin has 2 possible outcomes (heads or tails). For 6 tosses, the number of sample points in the sample space is 2^6 = 64.

Question 7

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 arrange 5 people is 5 factorial (5!), which equals 5 x 4 x 3 x 2 x 1 = 120.

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 number of ways to choose one of each item is found by multiplying the number of choices for each category together: 12 choices of table linens * 3 choices of china * 2 choices of flatware * 3 choices of stemware = 216 ways.

Question 9

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

Accepted Answer

Independent events can occur at the same time, while mutually exclusive events cannot happen simultaneously. Independence means the occurrence of one event does not affect the probability of the other, whereas mutual exclusivity means the occurrence of one event prevents the occurrence of the other.

Question 10

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

Accepted Answer

Two events are considered independent if the occurrence of one event does not affect the probability of the other event occurring. The mathematical expression of this relationship is $P(A \text{ and } B) = P(A) \times P(B)$, which means the probability of both events happening together is equal to the product of their individual probabilities.

Question 11

At a certain university, 70% of the students own cars. However, only 45% of the residence
hall students own cars. Are the events owning a car and living in a residence hall
independent? Explain.

Accepted Answer

The answer of At a certain university, 70% of the...

Question 12

A pair of fair dice is tossed. Events A and B are defined as follows.
A: {The sum of the numbers showing is odd}
B: {The sum of the numbers showing is 2, 11, or 12}
Are A and B independent events? Explain.

Accepted Answer

The answer of A pair of fair dice is tossed....

Question 13

Classify the events as dependent or independent: Events A and B where P(A)= 0.8, P(B)= 0.5, and P(A andB)= 0.39.

Accepted Answer

Events A and B are dependent because the probability of A and B occurring together (P(A and B) = 0.39) is not equal to the product of their individual probabilities (P(A) * P(B) = 0.8 * 0.5 = 0.4).

Question 14

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 15

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 16

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

Accepted Answer

The independence of events A and B means that the occurrence of one does not affect the probability of the occurrence of the other, which is mathematically represented as P(A and B) = P(A)P(B). It does not imply that P(A) = P(B).

Question 17

Two chips are drawn at random and without replacement from a bag containing two blue
chips and two red chips. Events A and B are defined as follows.
A: {Both chips are the same color}
B: {At least one of the chips is blue}
Are A and B independent events? Explain.

Accepted Answer

The answer of Two chips are drawn at random and...

Question 18

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

Question 19

On a certain statistics test, 20% of the students earned a score of 90 or above. It was also
true that 20% of the male students earned a score of 90 or above. Are the events earning a
score of 90 or above and being male independent? Explain.

Accepted Answer

The answer of On a certain statistics test, 20% of...

Question 20

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, and since there are 3 dice, the total number of sample points is $6 \times 6 \times 6 = 216$.

Quiz 3: Probability

In a box of 50 markers, 30 markers are either red or black, 20 are missing their caps, and 12 markers are either red or black and are missing their caps. Are the events ʺred or blackʺ and ʺmissing capʺ dependent or independent? Explain.

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?

Classify the events as dependent or independent: Events A and B where P(A) = 0.9, P(B) = 0.1, and P(A andB) = 0.09.

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

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

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?

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.

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

At a certain university, 70% of the students own cars. However, only 45% of the residence hall students own cars. Are the events owning a car and living in a residence hall independent? Explain.

A pair of fair dice is tossed. Events A and B are defined as follows. A: {The sum of the numbers showing is odd} B: {The sum of the numbers showing is 2, 11, or 12} Are A and B independent events? Explain.

Classify the events as dependent or independent: Events A and B where P(A) = 0.8, P(B) = 0.5, and P(A andB) = 0.39.

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?.

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

Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Events A and B are defined as follows. A: {Both chips are the same color} B: {At least one of the chips is blue} Are A and B independent events? Explain.

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?

On a certain statistics test, 20% of the students earned a score of 90 or above. It was also true that 20% of the male students earned a score of 90 or above. Are the events earning a score of 90 or above and being male independent? Explain.

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

Quiz 3: Probability

In a box of 50 markers, 30 markers are either red or black, 20 are missing their caps, and 12 markers are either red or black and are missing their caps. Are the events ʺred or blackʺ and ʺmissing capʺ dependent or independent? Explain.

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?

Classify the events as dependent or independent: Events A and B where P(A) = 0.9, P(B) = 0.1, and P(A andB) = 0.09.

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

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

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?

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.

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

At a certain university, 70% of the students own cars. However, only 45% of the residence hall students own cars. Are the events owning a car and living in a residence hall independent? Explain.

A pair of fair dice is tossed. Events A and B are defined as follows. A: {The sum of the numbers showing is odd} B: {The sum of the numbers showing is 2, 11, or 12} Are A and B independent events? Explain.

Classify the events as dependent or independent: Events A and B where P(A) = 0.8, P(B) = 0.5, and P(A andB) = 0.39.

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?.

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

Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Events A and B are defined as follows. A: {Both chips are the same color} B: {At least one of the chips is blue} Are A and B independent events? Explain.

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?

On a certain statistics test, 20% of the students earned a score of 90 or above. It was also true that 20% of the male students earned a score of 90 or above. Are the events earning a score of 90 or above and being male independent? Explain.

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

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