Question 1

A fair die is rolled. Find the probability that the result is a 4, given that the result is even. ​
A) 
B) 
C) 
D) 
E)0

Accepted Answer

The answer of A fair die is rolled. Find the...

Question 2

The following table gives the numbers of AIDS deaths in a single year for people over age 13 in various categories. Use the table to find the probability, rounded to four decimal places, that a person who died of AIDS in this year was Hispanic. ​  ​
A)Pr(Hispanic) = 0.7155
B)Pr(Hispanic) = 0.4771
C)Pr(Hispanic) = 0.2736
D)Pr(Hispanic) = 0.0652
E)Pr(Hispanic) = 0.1209

Accepted Answer

The answer of The following table gives the numbers of...

Question 3

The probability that a wife W watches a certain television show is 0.31, that her husband H watches it is 0.21, and that both watch the show is 0.05. What is the probability, to two decimal places, that either the husband or the wife watches this show? ​
A)Pr(H∪W) = 0.21
B)Pr(H∪W) = 0.05
C)Pr(H∪W) = 0.57
D)Pr(H∪W) = 0.47
E)Pr(H∪W) = 0.52

Accepted Answer

We need to find the probability of either the husband or the wife watching the show. This can be represented as the union of events H and W (i.e. H or W or both). We can use the formula:
Pr(H∪W) = Pr(H) + Pr(W) - Pr(H∩W)
where Pr(H∩W) represents the probability of both the husband and the wife watching the show. 
Substituting the given values:
Pr(H∪W) = 0.21 + 0.31 - 0.05 = 0.47
Therefore, the probability that either the husband or the wife watches the show is 0.47 or 47%. Therefore, the answer is D.

Question 4

A bag contains 7 red balls numbered 1-7 and 15 white balls numbered 8-22. One ball is drawn from the bag. What is the probability that the ball is red R, given that the ball is even-numbered E? ​
A)Pr(R | E) = 
B)Pr(R | E) = 
C)Pr(R | E) = 
D)Pr(R | E) = 
E)Pr(R | E) =

Accepted Answer

The answer of A bag contains 7 red balls numbered...

Question 5

Accepted Answer

The answer of A bag contains 11 red balls and...

Question 6

A mathematics class consists of 17 engineering majors E, 13 science majors S, and 9 liberal arts majors LA. Twelve of the engineering students, 3 of the science majors, and 3 of the liberal arts majors are female. What is the probability that a student selected at random is an engineering major or is a female F? ​
A)Pr(E∪F) = 
B)Pr(E∪F) = 
C)Pr(E∪F) = 
D)Pr(E∪F) = 
E)Pr(E∪F) =

Accepted Answer

There are a total of 17+13+9=39 students in the class. 
The number of female students is 12+3+3=18. 
To find the probability of selecting an engineering major or a female student, we need to add the number of engineering students and female students, but we also need to subtract the number of female engineering students since we counted them twice:

P(E∪F) = (17+18 - 12)/39 = 23/39

Therefore, the best choice is B.

Question 7

The following table gives the numbers of AIDS deaths in a single year for people over age 13 in various categories. Use the table to find the probability, rounded to four decimal places, that a person who died of AIDS in this year was female or Hispanic. ​  ​
A)Pr(female∪Hispanic) = 0.3589
B)Pr(female∪Hispanic) = 0.4876
C)Pr(female∪Hispanic) = 0.8089
D)Pr(female∪Hispanic) = 0.5260
E)Pr(female∪Hispanic) = 0.5683

Accepted Answer

The answer of The following table gives the numbers of...

Question 8

A box contains 3 red balls, 5 white balls, and 3 black balls. Two balls are drawn at random from the box with replacement of the first before the second is drawn.What is the probability of getting a red R ball on the first draw and a white W ball on the second? ​
A)Pr(R first ∩ W second) = 
B)Pr(R first ∩ W second) = 
C)Pr(R first ∩ W second) = 
D)Pr(R first ∩ W second) = 
E)Pr(R first ∩ W second) =

Accepted Answer

The probability of drawing a red ball first is 3/11. 
Since the ball is replaced, the probability of drawing a white ball second is 5/11.
The probability of both events happening together is the product of the individual probabilities:
Pr(R first ∩ W second) = (3/11) x (5/11) = 15/121
Therefore, the correct answer is B.

Question 9

The following table gives the numbers of AIDS deaths in a single year for people over age 13 in various categories. Use the table to find the probability, rounded to four decimal places, that a person who died of AIDS in this year was female. ​  ​
A)Pr(female) = 0.5758
B)Pr(female) = 0.4242
C)Pr(female) = 0.5601
D)Pr(female) = 0.3664
E)Pr(female) = 0.6179

Accepted Answer

The answer of The following table gives the numbers of...

Question 10

A fair die is thrown twice. What is the probability that a 3 will result the first time and a 2 the second time? ​
A)Pr(3 first ∩ 2 second) = 
B)Pr(3 first ∩ 2 second) = 
C)Pr(3 first ∩ 2 second) = 
D)Pr(3 first ∩ 2 second) = 
E)Pr(3 first ∩ 2 second) =

Accepted Answer

The answer of A fair die is thrown twice. What...

Question 11

Suppose that a person groups 18 objects into three groups in such a way that ​
6 objects are in group A.
6 objects are in group B.
7 objects are in group C.
3 objects are in both group A and group B.
5 objects are in both group B and group C.
4 objects are in both group A and group C.
2 objects are in all three groups.
​
What is the probability that an object chosen at random has been placed in group A or group B?
​
A) 
B) 
C) 
D) 
E)0

Accepted Answer

The answer of Suppose that a person groups 18 objects...

Question 12

A bag contains 9 red balls and 15 white balls. Two balls are drawn without replacement. What is the probability that the second ball is red R, given that the first ball is white W? ​
A)  
B)  
C)  
D)  
E)

Accepted Answer

The answer of A bag contains 9 red balls and...

Question 13

A mathematics class consists of 14 engineering majors E, 8 science majors S, and 15 liberal arts majors LA. What is the probability that a student selected at random will be an engineering or science major? ​
A)Pr(E∪S) = 
B)Pr(E∪S) = 
C)Pr(E∪S) = 
D)Pr(E∪S) = 
E)Pr(E∪S) =

Accepted Answer

The answer of A mathematics class consists of 14 engineering...

Question 14

A bag contains 4 red balls and 11 white balls. Two balls are drawn from the bag. What is the probability that the second ball is white W, given that the first ball is red and is replaced before the second is drawn? ​
A)Pr(W) = 
B)Pr(W) = 
C)Pr(W) = 
D)Pr(W) = 
E)Pr(W) =

Accepted Answer

To find the probability of the second ball being white given that the first ball was red and is replaced before the second is drawn, we need to use the formula for conditional probability:
P(W|R) = P(W and R) / P(R)
where W and R denote the events of drawing a white and red ball respectively.

Since the first ball is replaced before the second is drawn, the probability of drawing a red ball on the first draw is 4 / 15 (since there are 4 red balls out of 15 total). 
The probability of drawing a white ball on the second draw, given that a red ball was drawn first and replaced, is 11 / 15 (since there are still 11 white balls out of 15 total).
The probability of both events happening (drawing a red ball first and a white ball second) is simply the product of the separate probabilities: (4 / 15) * (11 / 15) = 44 / 225.

Therefore, 
P(W|R) = (11 / 15) / (4 / 15) = 11 / 4 = 11eb0d3b_9827_5d00_9790_65e68dbf2971_TB1243_11.

Question 15

The following table gives the percent of employees of the Ace Company in each of three salary brackets, categorized by the sex of the employees. An employee is selected at random. What is the probability that the person is male or makes less than $30,000? ​  ​
A)Pr(male∪$30,000) = 0.84
B)Pr(male∪$30,000) = 0.55
C)Pr(male∪$30,000) = 0.29
D)Pr(male∪$30,000) = 0.78
E)Pr(male∪$30,000) = 0.47

Accepted Answer

The answer of The following table gives the percent of...

Question 16

The following table gives the numbers of AIDS deaths in a single year for people over age 13 in various categories. Use the table to find the probability, rounded to four decimal places, that a person who died of AIDS in this year was male or black (non-Hispanic). ​  ​
A)Pr(male∪black) = 0.4486
B)Pr(male∪black) = 0.5983
C)Pr(male∪black) = 0.7894
D)Pr(male∪black) = 0.6946
E)Pr(male∪black) = 0.6325

Accepted Answer

The answer of The following table gives the numbers of...

Question 17

A mathematics class consists of 9 engineering majors E, 14 science majors S, and 8 liberal arts majors LA. What is the probability that a student selected at random will be a science or liberal arts major? ​
A)Pr(S∪LA) = 
B)Pr(S∪LA) = 
C)Pr(S∪LA) = 
D)Pr(S∪LA) = 
E)Pr(S∪LA) =

Accepted Answer

The answer of A mathematics class consists of 9 engineering...

Question 18

The following table gives the percent of employees of the Ace Company in each of three salary brackets, categorized by the sex of the employees. An employee is selected at random. What is the probability that the person selected is female and makes less than $30,000? ​  ​
A)Pr(female∩less than $30,000) = 0.34
B)Pr(female∩less than $30,000) = 0.21
C)Pr(female∩less than $30,000) = 0.54
D)Pr(female∩less than $30,000) = 0.55
E)Pr(female∩less than $30,000) = 0.33

Accepted Answer

From the table, we see that the percentage of female employees in the less than $30,000 salary bracket is 35%, so the probability of selecting a female employee from this bracket is 0.35. Therefore, the probability of selecting a female employee who makes less than $30,000 is Pr(female∩less than $30,000) = 0.35 x 0.6 = 0.21.

Question 19

The following table gives the percent of employees of the Ace Company in each of three salary brackets, categorized by the sex of the employees. An employee is selected at random. What is the probability that the person selected makes at least $50,000? ​  ​
A)Pr(at least $50,000) = 0.31
B)Pr(at least $50,000) = 0.36
C)Pr(at least $50,000) = 0.50
D)Pr(at least $50,000) = 0.33
E)Pr(at least $50,000) = 0.57

Accepted Answer

The answer of The following table gives the percent of...

Question 20

Of 100 students, 26 can speak French F, 33 can speak German G, and 16 can speak both French and German. If a student is picked at random, what is the probability that he or she can speak French or German? ​
A)Pr(F∪G) = 
B)Pr(F∪G) = 
C)Pr(F∪G) = 
D)Pr(F∪G) = 
E)Pr(F∪G) =

Accepted Answer

The answer of Of 100 students, 26 can speak French...

Quiz 8: Introduction to Probability

A fair die is rolled. Find the probability that the result is a 4, given that the result is even.

The following table gives the numbers of AIDS deaths in a single year for people over age 13 in various categories. Use the table to find the probability, rounded to four decimal places, that a person who died of AIDS in this year was Hispanic.

The probability that a wife W watches a certain television show is 0.31, that her husband H watches it is 0.21, and that both watch the show is 0.05. What is the probability, to two decimal places, that either the husband or the wife watches this show?

A bag contains 7 red balls numbered 1-7 and 15 white balls numbered 8-22. One ball is drawn from the bag. What is the probability that the ball is red R, given that the ball is even-numbered E?

A bag contains 11 red balls and 13 white balls. Two balls are drawn without replacement. What is the probability that the second ball is white W, given that the first ball is red R?

The following table gives the numbers of AIDS deaths in a single year for people over age 13 in various categories. Use the table to find the probability, rounded to four decimal places, that a person who died of AIDS in this year was female or Hispanic.

A box contains 3 red balls, 5 white balls, and 3 black balls. Two balls are drawn at random from the box with replacement of the first before the second is drawn.What is the probability of getting a red R ball on the first draw and a white W ball on the second?

The following table gives the numbers of AIDS deaths in a single year for people over age 13 in various categories. Use the table to find the probability, rounded to four decimal places, that a person who died of AIDS in this year was female.

A fair die is thrown twice. What is the probability that a 3 will result the first time and a 2 the second time?

A bag contains 9 red balls and 15 white balls. Two balls are drawn without replacement. What is the probability that the second ball is red R, given that the first ball is white W?

A mathematics class consists of 14 engineering majors E, 8 science majors S, and 15 liberal arts majors LA. What is the probability that a student selected at random will be an engineering or science major?

A bag contains 4 red balls and 11 white balls. Two balls are drawn from the bag. What is the probability that the second ball is white W, given that the first ball is red and is replaced before the second is drawn?

The following table gives the percent of employees of the Ace Company in each of three salary brackets, categorized by the sex of the employees. An employee is selected at random. What is the probability that the person is male or makes less than $30,000?

The following table gives the numbers of AIDS deaths in a single year for people over age 13 in various categories. Use the table to find the probability, rounded to four decimal places, that a person who died of AIDS in this year was male or black (non-Hispanic) .

A mathematics class consists of 9 engineering majors E, 14 science majors S, and 8 liberal arts majors LA. What is the probability that a student selected at random will be a science or liberal arts major?

The following table gives the percent of employees of the Ace Company in each of three salary brackets, categorized by the sex of the employees. An employee is selected at random. What is the probability that the person selected is female and makes less than $30,000?

The following table gives the percent of employees of the Ace Company in each of three salary brackets, categorized by the sex of the employees. An employee is selected at random. What is the probability that the person selected makes at least $50,000?

Of 100 students, 26 can speak French F, 33 can speak German G, and 16 can speak both French and German. If a student is picked at random, what is the probability that he or she can speak French or German?

Quiz 8: Introduction to Probability

A fair die is rolled. Find the probability that the result is a 4, given that the result is even. ​

The following table gives the numbers of AIDS deaths in a single year for people over age 13 in various categories. Use the table to find the probability, rounded to four decimal places, that a person who died of AIDS in this year was Hispanic. ​ ​

The probability that a wife W watches a certain television show is 0.31, that her husband H watches it is 0.21, and that both watch the show is 0.05. What is the probability, to two decimal places, that either the husband or the wife watches this show? ​

A bag contains 7 red balls numbered 1-7 and 15 white balls numbered 8-22. One ball is drawn from the bag. What is the probability that the ball is red R, given that the ball is even-numbered E? ​

A bag contains 11 red balls and 13 white balls. Two balls are drawn without replacement. What is the probability that the second ball is white W, given that the first ball is red R? ​

The following table gives the numbers of AIDS deaths in a single year for people over age 13 in various categories. Use the table to find the probability, rounded to four decimal places, that a person who died of AIDS in this year was female or Hispanic. ​ ​

A box contains 3 red balls, 5 white balls, and 3 black balls. Two balls are drawn at random from the box with replacement of the first before the second is drawn.What is the probability of getting a red R ball on the first draw and a white W ball on the second? ​

The following table gives the numbers of AIDS deaths in a single year for people over age 13 in various categories. Use the table to find the probability, rounded to four decimal places, that a person who died of AIDS in this year was female. ​ ​

A fair die is thrown twice. What is the probability that a 3 will result the first time and a 2 the second time? ​

A bag contains 9 red balls and 15 white balls. Two balls are drawn without replacement. What is the probability that the second ball is red R, given that the first ball is white W? ​

A mathematics class consists of 14 engineering majors E, 8 science majors S, and 15 liberal arts majors LA. What is the probability that a student selected at random will be an engineering or science major? ​

A bag contains 4 red balls and 11 white balls. Two balls are drawn from the bag. What is the probability that the second ball is white W, given that the first ball is red and is replaced before the second is drawn? ​

The following table gives the percent of employees of the Ace Company in each of three salary brackets, categorized by the sex of the employees. An employee is selected at random. What is the probability that the person is male or makes less than $30,000? ​ ​

The following table gives the numbers of AIDS deaths in a single year for people over age 13 in various categories. Use the table to find the probability, rounded to four decimal places, that a person who died of AIDS in this year was male or black (non-Hispanic) . ​ ​

A mathematics class consists of 9 engineering majors E, 14 science majors S, and 8 liberal arts majors LA. What is the probability that a student selected at random will be a science or liberal arts major? ​

The following table gives the percent of employees of the Ace Company in each of three salary brackets, categorized by the sex of the employees. An employee is selected at random. What is the probability that the person selected is female and makes less than $30,000? ​ ​

The following table gives the percent of employees of the Ace Company in each of three salary brackets, categorized by the sex of the employees. An employee is selected at random. What is the probability that the person selected makes at least $50,000? ​ ​

Of 100 students, 26 can speak French F, 33 can speak German G, and 16 can speak both French and German. If a student is picked at random, what is the probability that he or she can speak French or German? ​

A fair die is rolled. Find the probability that the result is a 4, given that the result is even.

The following table gives the numbers of AIDS deaths in a single year for people over age 13 in various categories. Use the table to find the probability, rounded to four decimal places, that a person who died of AIDS in this year was Hispanic.

The probability that a wife W watches a certain television show is 0.31, that her husband H watches it is 0.21, and that both watch the show is 0.05. What is the probability, to two decimal places, that either the husband or the wife watches this show?

A bag contains 7 red balls numbered 1-7 and 15 white balls numbered 8-22. One ball is drawn from the bag. What is the probability that the ball is red R, given that the ball is even-numbered E?

A bag contains 11 red balls and 13 white balls. Two balls are drawn without replacement. What is the probability that the second ball is white W, given that the first ball is red R?

The following table gives the numbers of AIDS deaths in a single year for people over age 13 in various categories. Use the table to find the probability, rounded to four decimal places, that a person who died of AIDS in this year was female or Hispanic.

A box contains 3 red balls, 5 white balls, and 3 black balls. Two balls are drawn at random from the box with replacement of the first before the second is drawn.What is the probability of getting a red R ball on the first draw and a white W ball on the second?

The following table gives the numbers of AIDS deaths in a single year for people over age 13 in various categories. Use the table to find the probability, rounded to four decimal places, that a person who died of AIDS in this year was female.

A fair die is thrown twice. What is the probability that a 3 will result the first time and a 2 the second time?

A bag contains 9 red balls and 15 white balls. Two balls are drawn without replacement. What is the probability that the second ball is red R, given that the first ball is white W?

A mathematics class consists of 14 engineering majors E, 8 science majors S, and 15 liberal arts majors LA. What is the probability that a student selected at random will be an engineering or science major?

A bag contains 4 red balls and 11 white balls. Two balls are drawn from the bag. What is the probability that the second ball is white W, given that the first ball is red and is replaced before the second is drawn?

The following table gives the percent of employees of the Ace Company in each of three salary brackets, categorized by the sex of the employees. An employee is selected at random. What is the probability that the person is male or makes less than $30,000?

The following table gives the numbers of AIDS deaths in a single year for people over age 13 in various categories. Use the table to find the probability, rounded to four decimal places, that a person who died of AIDS in this year was male or black (non-Hispanic) .

A mathematics class consists of 9 engineering majors E, 14 science majors S, and 8 liberal arts majors LA. What is the probability that a student selected at random will be a science or liberal arts major?

The following table gives the percent of employees of the Ace Company in each of three salary brackets, categorized by the sex of the employees. An employee is selected at random. What is the probability that the person selected is female and makes less than $30,000?

The following table gives the percent of employees of the Ace Company in each of three salary brackets, categorized by the sex of the employees. An employee is selected at random. What is the probability that the person selected makes at least $50,000?

Of 100 students, 26 can speak French F, 33 can speak German G, and 16 can speak both French and German. If a student is picked at random, what is the probability that he or she can speak French or German?