Question 1

At Dolon General Hospital,30 percent of the patients have Medicare insurance (M)while 70 percent do not have Medicare insurance (M´).Twenty percent of the Medicare patients arrive by ambulance,compared with 10 percent of the non-Medicare patients.If a patient arrives by ambulance,what is the probability that the patient has Medicare insurance?
A) .7000
B) .5000
C) .4615
D) .1300

Accepted Answer

Question 2

The number of unique orders in which five items (A,B,C,D,E)can be arranged is:
A) 5.
B) 840.
C) 120.
D) 24.

Accepted Answer

The number of unique arrangements for a set of n items is n factorial (n!), which is the product of all positive integers from 1 to n. Therefore, the number of unique orders in which five items can be arranged is 5! = 120. Option A is incorrect, as there are more than 5 unique orders possible. Option B is incorrect, as the number 840 is not a factor of 5. Option D is incorrect, as there are more than 24 unique orders possible.

Question 3

If each of two independent file servers has a reliability of 93 percent and either alone can run the website,then the overall website availability is:
A) .9951.
B) .8649.
C) .9300.
D) .9522.

Accepted Answer

The overall availability is calculated by considering the probability that both servers fail, which is 0.07 * 0.07 = 0.0049. Subtracting this from 1 gives 0.9951 or 99.51% availability.

Question 4

Which best exemplifies the classical definition of probability?
A) The probability that a male aged 50 will have an accident in a week's car rental at Alamo
B) The probability that a pair of dice will come up 7 when they are rolled
C) The probability that the winter Olympic games will be held in Europe in 2022
D) The probability that a checked bag on Flight 1872 will weigh more than 30 pounds

Accepted Answer

The classical definition of probability is based on the assumption that all outcomes are equally likely. Rolling a pair of dice is a classic example of this, as each of the 6 possible faces on each die is equally likely to come up, making the total number of possible outcomes, or sample space, equal to 6 x 6 = 36. Of these outcomes, only 6 correspond to rolling a 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), so the probability of rolling a 7 is 6/36 or 1/6.

Question 5

Which best exemplifies a subjective probability?
A) The probability that a female aged 30 will have an accident in a week's car rental at Hertz.
B) The probability that a pair of dice will come up 7 in a given throw.
C) The probability that the summer Olympic games will be held in Chicago in 2020.
D) The probability that a checked bag on Flight 1872 will weigh more than 40 pounds.

Accepted Answer

Subjective probability is based on personal judgment or opinion rather than objective data. The probability of the Olympic games being held in a specific city is based on personal belief or speculation, not on statistical analysis.

Question 6

How many ways can we choose three items at random without replacement from five items (A,B,C,D,E)if the order of the selected items is not important?
A) 60
B) 120
C) 10
D) 24

Accepted Answer

The number of combinations of choosing three items out of five is given by 5 choose 3 which is equal to (5!)/(3!(5-3)!) = 10. Since the order of the selected items is not important, we do not need to consider permutations which would have been necessary if the order was important. Therefore, the answer is 10 or choice letter C.

Question 7

From the following tree,find the probability that a randomly chosen person will get the flu vaccine and will also get the flu. 
A) .10
B) .07
C) .19
D) .70

Accepted Answer

The probability of getting the flu vaccine and also getting the flu is the probability of following the path from the start node to the "Flu Vaccine and Flu" endpoint. This path has a probability of .07.

Question 8

From the following tree,find the probability that a randomly chosen person will not get a vaccination and will not get the flu. 
A) .18
B) .60
C) .19
D) .70

Accepted Answer

The answer of From the following tree,find the probability that...

Question 9

Which statement is false?
A) If P(A)= .05,then the odds against event A's occurrence are 19 to 1.
B) If A and B are mutually exclusive events,then P(A or B)= 0.
C) The number of permutations of five things taken two at a time is 20.

Accepted Answer

B) is false because if A and B are mutually exclusive events, then P(A or B) = P(A) + P(B), not 0. This means the probability of either event A or event B occurring is the sum of their individual probabilities, assuming they cannot both occur at the same time.

Question 10

In a certain city,5 percent of all drivers have expired licenses and 10 percent have an unpaid parking ticket.If these events are independent,what is the probability that a driver has both an expired license and an unpaid parking ticket?
A) .010
B) .005
C) .001
D) Cannot be determined

Accepted Answer

Since the events are independent, we can simply multiply their probabilities to find the probability of both events occurring:
P(expired license and unpaid parking ticket) = P(expired license) * P(unpaid parking ticket) = 0.05 * 0.1 = 0.005. Therefore, the answer is choice B).

Question 11

The probability that event A occurs,given that event B has occurred,is an example of:
A) a marginal probability.
B) a conditional probability.
C) a joint probability.
D) more than one of the above.

Accepted Answer

The given scenario represents conditional probability, which is the probability of an event occurring given that another event has already occurred. Marginal probability refers to the probability of a single event occurring, without regard to any other events. Joint probability refers to the probability of two or more events occurring simultaneously.

Question 12

In a certain city,5 percent of all drivers have expired licenses,10 percent have an unpaid parking ticket,and 1 percent have both an expired license and an unpaid parking ticket.Are these events independent?
A) No
B) Yes
C) Can't tell from given information

Accepted Answer

Since 1 percent of drivers have both an expired license and an unpaid parking ticket, the events are not independent. Knowing that a driver has one event affects the probability of them having the other event. Therefore, the answer is A) No, the events are not independent.

Question 13

At Joe's Restaurant,80 percent of the diners are new customers (N),while 20 percent are returning customers (R).Fifty percent of the new customers pay by credit card,compared with 70 percent of the regular customers.If a customer pays by credit card,what is the probability that the customer is a new customer?
A) .7407
B) .8000
C) .5400
D) .5000

Accepted Answer

To find the probability that a customer is a new customer given they pay by credit card, we use Bayes' theorem or a basic probability approach. Let's calculate:- Probability of a new customer (P(N)) = 80% or 0.8- Probability of a returning customer (P(R)) = 20% or 0.2- Probability of paying by credit card given a new customer (P(C|N)) = 50% or 0.5- Probability of paying by credit card given a returning customer (P(C|R)) = 70% or 0.7First, find the overall probability of paying by credit card, P(C), which is the sum of the probabilities of being a new or returning customer and paying by credit card:P(C) = P(N) * P(C|N) + P(R) * P(C|R)     = 0.8 * 0.5 + 0.2 * 0.7     = 0.4 + 0.14     = 0.54Then, the probability that a customer is a new customer given they pay by credit card, P(N|C), is:P(N|C) = [P(N) * P(C|N)] / P(C)       = (0.8 * 0.5) / 0.54       = 0.4 / 0.54       ≈ 0.7407 or 74.07%So, the correct answer is A) 0.7407.

Question 14

From the following tree,find the probability that a randomly chosen person will get the flu. 
A) .19
B) .07
C) .81
D) .70

Accepted Answer

The answer of From the following tree,find the probability that...

Question 15

If two events are collectively exhaustive,what is the probability that one or the other will occur?
A) 1.00
B) 0.00
C) 0.50
D) Can't tell from given information

Accepted Answer

When two events are collectively exhaustive, it means that at least one of the events must occur, making the probability that one or the other will occur 1.00.

Question 16

If four items are chosen at random without replacement from seven items,in how many ways can the four items be arranged,treating each arrangement as a different event (i.e. ,if order is important)?
A) 35
B) 840
C) 5040
D) 24

Accepted Answer

First, choose 4 items out of 7, which can be done in 7C4 ways (combination formula: 7! / [4!(7-4)!] = 35 ways). Then, arrange these 4 items, which can be done in 4! (factorial) ways = 24 ways. Multiplying these together gives 35 * 24 = 840 ways.

Question 17

Which best exemplifies the empirical definition of probability?
A) The probability that a Chinese athlete will win the diving competition in the next Olympics
B) The probability that a fair coin will come up heads when it is flipped
C) The probability that your own bank will become insolvent within 12 months
D) The probability that a checked bag on Flight 1872 will weigh less than 30 pounds

Accepted Answer

The answer of Which best exemplifies the empirical definition of...

Question 18

The value of ₆C₂ is: A) 15. B) 30. C) 720.

Accepted Answer

The value of 6C2, which represents the number of combinations of 6 items taken 2 at a time, is calculated using the formula 6! / (2!(6-2)!) = 15.

Question 19

A baseball player said,"Yes,I'm in a batting slump.But the law of averages has got to catch up sooner or later.I'm bound to improve." Discuss the logic of this statement.

Accepted Answer

The answer of A baseball player said,"Yes,I'm in a batting...

Question 20

Axolotl,Inc.decided to double the number of independent network file servers,each server being capable of running its entire internal corporate network.Bob suggested that "doubling the number of file servers in our corporate network will just double the chances of failure." Is Bob right? Has the company made an error?

Accepted Answer

The answer of Axolotl,Inc.decided to double the number of independent...

Quiz 5: Probability

The number of unique orders in which five items (A,B,C,D,E) can be arranged is:

If each of two independent file servers has a reliability of 93 percent and either alone can run the website,then the overall website availability is:

Which best exemplifies the classical definition of probability?

Which best exemplifies a subjective probability?

How many ways can we choose three items at random without replacement from five items (A,B,C,D,E) if the order of the selected items is not important?

From the following tree,find the probability that a randomly chosen person will get the flu vaccine and will also get the flu.

From the following tree,find the probability that a randomly chosen person will not get a vaccination and will not get the flu.

Which statement is false?

In a certain city,5 percent of all drivers have expired licenses and 10 percent have an unpaid parking ticket.If these events are independent,what is the probability that a driver has both an expired license and an unpaid parking ticket?

The probability that event A occurs,given that event B has occurred,is an example of:

In a certain city,5 percent of all drivers have expired licenses,10 percent have an unpaid parking ticket,and 1 percent have both an expired license and an unpaid parking ticket.Are these events independent?

From the following tree,find the probability that a randomly chosen person will get the flu.

If two events are collectively exhaustive,what is the probability that one or the other will occur?

If four items are chosen at random without replacement from seven items,in how many ways can the four items be arranged,treating each arrangement as a different event (i.e. ,if order is important) ?

Which best exemplifies the empirical definition of probability?

The value of ₆C₂ is:

A baseball player said,"Yes,I'm in a batting slump.But the law of averages has got to catch up sooner or later.I'm bound to improve." Discuss the logic of this statement.

Quiz 5: Probability

The number of unique orders in which five items (A,B,C,D,E) can be arranged is:

If each of two independent file servers has a reliability of 93 percent and either alone can run the website,then the overall website availability is:

Which best exemplifies the classical definition of probability?

Which best exemplifies a subjective probability?

How many ways can we choose three items at random without replacement from five items (A,B,C,D,E) if the order of the selected items is not important?

From the following tree,find the probability that a randomly chosen person will get the flu vaccine and will also get the flu.

From the following tree,find the probability that a randomly chosen person will not get a vaccination and will not get the flu.

Which statement is false?

In a certain city,5 percent of all drivers have expired licenses and 10 percent have an unpaid parking ticket.If these events are independent,what is the probability that a driver has both an expired license and an unpaid parking ticket?

The probability that event A occurs,given that event B has occurred,is an example of:

In a certain city,5 percent of all drivers have expired licenses,10 percent have an unpaid parking ticket,and 1 percent have both an expired license and an unpaid parking ticket.Are these events independent?

From the following tree,find the probability that a randomly chosen person will get the flu.

If two events are collectively exhaustive,what is the probability that one or the other will occur?

If four items are chosen at random without replacement from seven items,in how many ways can the four items be arranged,treating each arrangement as a different event (i.e. ,if order is important) ?

Which best exemplifies the empirical definition of probability?

The value of 6C2 is:

A baseball player said,"Yes,I'm in a batting slump.But the law of averages has got to catch up sooner or later.I'm bound to improve." Discuss the logic of this statement.

The value of ₆C₂ is: