Question 1

Consider a standard deck of 52 playing cards,a randomly selected card from the deck,and the following events: R = red,B = black,A = ace,N = nine,D = diamond and C = club. For each of the following pair of events,indicated whether the events are mutually exclusive
A and N
A)Yes,Mutually exclusive
B)No,not mutually exclusive

Accepted Answer

The events A and N are not mutually exclusive because it is possible for a card to be both an ace and a nine. For example, the ace of spades is both an ace and a nine.

Question 2

At a certain university,30% of the students major in zoology.Of the students majoring in zoology,60% are males.Of all the students at the university,70% are males. What is the probability that one randomly selected student is a male or is majoring in zoology?
A)1.00
B)0.60
C)0.21
D)0.18
E)0.82

Accepted Answer

(.30)+ (.70)-(.18)= .82

Question 3

In a major Midwestern university,55% of all undergraduates are female,25% belong to a Greek organization (fraternity or sorority)and 40% of all males belong to a Greek organization. Are the events "female/not female" and "belongs to a Greek organization" independent?
A)Yes,independent
B)No,not independent

Accepted Answer

P(G|F)P(G)

Question 4

At a certain university,30% of the students major in zoology.Of the students majoring in zoology,60% are males.Of all the students at the university,70% are males. What percentage of the students are males majoring in zoology?
A)60%
B)42%
C)12%
D)18%
E)70%

Accepted Answer

The answer of At a certain university,30% of the students...

Question 5

Consider a standard deck of 52 playing cards,a randomly selected card from the deck,and the following events: R = red,B = black,A = ace,N = nine,D = diamond and C = club. For each of the following pair of events,indicated whether the events are mutually exclusive
D and C
A)Yes,Mutually exclusive
B)No,not mutually exclusive

Accepted Answer

The events D (diamond) and C (club) are mutually exclusive because a card cannot be both a diamond and a club at the same time. They are two different suits and are disjoint sets. Therefore, there is no overlap between the two events, and they are mutually exclusive.

Question 6

At a certain university,30% of the students major in zoology.Of the students majoring in zoology,60% are males.Of all the students at the university,70% are males. Are the events "male" and "majoring in zoology" independent?
A)Yes,independent
B)No,not independent

Accepted Answer

P(M|Z)F1F1F1S1F1F1F10 P(M)

Question 7

At a certain university,30% of the students major in zoology.Of the students majoring in zoology,60% are males.Of all the students at the university,70% are males. What proportions of the males are majoring in zoology?
A).26
B).18
C).21
D).86
E).60

Accepted Answer

P(Z|M)= .18/.70 = .257

Question 8

Suppose that A₁ ,A₂ and B are events where A₁ and A₂ are mutually exclusive events and P(A₁)= .7 P(A₂)= .3 P(B│A₁)= .2 P(B│A₂)= .4 Find P(B) A)0.60 B)0.26 C)0.21 D)0.14 E)0.28

Accepted Answer

P(B)= P(A₁)* P(B│A₁)+ P(A₂)* P(B│A₂)= (.7)(.2)+ (.3)(.4)= .26

Question 9

Consider a standard deck of 52 playing cards,a randomly selected card from the deck,and the following events: R = red,B = black,A = ace,N = nine,D = diamond and C = club. For each of the following pair of events,indicated whether the events are mutually exclusive
R and C
A)Yes,mutually exclusive
B)No,not mutually exclusive

Accepted Answer

Red cards are either hearts or diamonds, while clubs are black. Therefore, a red card cannot be a club, making the events mutually exclusive.

Question 10

An advertising campaign is being developed to promote a new bookstore opening in the newest mall development.To develop an appropriate mailing list it has been decided to purchase lists of credit card holders from MasterCard and American Express.Combining the lists they find the following: 40% of the people on the list have only a MasterCard and 10% have only an American Express card.Another 20% hold both MasterCard and American Express.Finally,30% of those on the list have neither card.Suppose a person on the list is known to have a MasterCard.What is the probability that person also has an American Express Card?
A).20
B).33
C).18
D).70
E).90

Accepted Answer

We are given that 40% have only a MasterCard, 10% have only an American Express, and 20% have both. That means the percentage of people with a MasterCard is 40% + 20% = 60%. 
We are asked for the probability that a person with a MasterCard also has an American Express. This can be found using conditional probability: 
P(AmEx | MasterCard) = P(AmEx and MasterCard) / P(MasterCard) 
We already know that P(MasterCard) = 60%. To find P(AmEx and MasterCard), we can use the information that 20% have both. So, 
P(AmEx and MasterCard) = 20% 
Substituting these values, we get: 
P(AmEx | MasterCard) = 20% / 60% = 1/3 = 0.33 
Therefore, the answer is B) 33.

Question 11

Consider a standard deck of 52 playing cards,a randomly selected card from the deck,and the following events: R = red,B = black,A = ace,N = nine,D = diamond and C = club. For each of the following pair of events,indicate whether the events are mutually exclusive
R and A
A)Yes,mutually exclusive
B)No,not mutually exclusive

Accepted Answer

The events R (red) and A (ace) are not mutually exclusive because there are red aces (Ace of Hearts and Ace of Diamonds) in the deck.

Question 12

Consider a standard deck of 52 playing cards,a randomly selected card from the deck,and the following events: R = red,B = black,A = ace,N = nine,D = diamond and C = club. For each of the following pair of events,indicated whether the events are mutually exclusive
N and C
A)Yes,Mutually exclusive
B)No,not mutually exclusive

Accepted Answer

The events N (nine) and C (club) are not mutually exclusive because a card can be both a nine and a club, specifically the nine of clubs.

Question 13

In a major Midwestern university,55% of all undergraduates are female,25% belong to a Greek organization (fraternity or sorority)and 40% of all males belong to a Greek organization. What is the probability that an undergraduate is in a Greek organization given that the undergraduate is a female?
A).07
B).55
C).127
D).039
E)138

Accepted Answer

P(G|F)= .07/.55 = .127

Question 14

Suppose that A₁,A₂ and B are events where A₁ and A₂ are mutually exclusive events and P(A₁)= .7 P(A₂)= .3 P(B│A₁)= .2 P(B│A₂)= .4 Find P(A₂│B) A)0.12 B)0.26 C)0.21 D)0.14 E)0.46

Accepted Answer

P(A₂│B)= P(A₂ F1F1F1S1F1F1F10 B)/ P(B)= .12/26 = .46

Question 15

Suppose that A₁,A₂ and B are events where A₁ and A₂ are mutually exclusive events and P(A₁)= .7 P(A₂)= .3 P(B│A₁)= .2 P(B│A₂)= .4 Find P(A₁│B) A)0.12 B)0.26 C)0.21 D)0.14 E)0.28

Accepted Answer

P(A₁│B)= P(A₁ F1F1F1S1F1F1F10 B)/ P(B)= .14/.26 = .54

Quiz 4: Probability

Consider a standard deck of 52 playing cards,a randomly selected card from the deck,and the following events: R = red,B = black,A = ace,N = nine,D = diamond and C = club. For each of the following pair of events,indicated whether the events are mutually exclusive A and N

At a certain university,30% of the students major in zoology.Of the students majoring in zoology,60% are males.Of all the students at the university,70% are males. What is the probability that one randomly selected student is a male or is majoring in zoology?

In a major Midwestern university,55% of all undergraduates are female,25% belong to a Greek organization (fraternity or sorority) and 40% of all males belong to a Greek organization. Are the events "female/not female" and "belongs to a Greek organization" independent?

At a certain university,30% of the students major in zoology.Of the students majoring in zoology,60% are males.Of all the students at the university,70% are males. What percentage of the students are males majoring in zoology?

Consider a standard deck of 52 playing cards,a randomly selected card from the deck,and the following events: R = red,B = black,A = ace,N = nine,D = diamond and C = club. For each of the following pair of events,indicated whether the events are mutually exclusive D and C

At a certain university,30% of the students major in zoology.Of the students majoring in zoology,60% are males.Of all the students at the university,70% are males. Are the events "male" and "majoring in zoology" independent?

At a certain university,30% of the students major in zoology.Of the students majoring in zoology,60% are males.Of all the students at the university,70% are males. What proportions of the males are majoring in zoology?

Suppose that A₁ ,A₂ and B are events where A₁ and A₂ are mutually exclusive events and P(A₁) = .7 P(A₂) = .3 P(B│A₁) = .2 P(B│A₂) = .4 Find P(B)

Consider a standard deck of 52 playing cards,a randomly selected card from the deck,and the following events: R = red,B = black,A = ace,N = nine,D = diamond and C = club. For each of the following pair of events,indicated whether the events are mutually exclusive R and C

Consider a standard deck of 52 playing cards,a randomly selected card from the deck,and the following events: R = red,B = black,A = ace,N = nine,D = diamond and C = club. For each of the following pair of events,indicate whether the events are mutually exclusive R and A

Consider a standard deck of 52 playing cards,a randomly selected card from the deck,and the following events: R = red,B = black,A = ace,N = nine,D = diamond and C = club. For each of the following pair of events,indicated whether the events are mutually exclusive N and C

In a major Midwestern university,55% of all undergraduates are female,25% belong to a Greek organization (fraternity or sorority) and 40% of all males belong to a Greek organization. What is the probability that an undergraduate is in a Greek organization given that the undergraduate is a female?

Suppose that A₁,A₂ and B are events where A₁ and A₂ are mutually exclusive events and P(A₁) = .7 P(A₂) = .3 P(B│A₁) = .2 P(B│A₂) = .4 Find P(A₂│B)

Suppose that A₁,A₂ and B are events where A₁ and A₂ are mutually exclusive events and P(A₁) = .7 P(A₂) = .3 P(B│A₁) = .2 P(B│A₂) = .4 Find P(A₁│B)