Question 1

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 2

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)0.010
B)0.005
C)0.001
D)Cannot be determined

Accepted Answer

If the events are independent, then we can multiply their probabilities to find the probability of both events happening together.

Let D be the event of having an expired license and P be the event of having an unpaid parking ticket.

P(D) = 0.05 (given) 
P(P) = 0.10 (given)

Since the events are independent: 
P(D and P) = P(D) * P(P)

P(D and P) = 0.05 * 0.10

P(D and P) = 0.005 or 0.5%

Therefore, the probability of a driver having both an expired license and an unpaid parking ticket is 0.005 or 0.5%.

The best choice is B.

Question 3

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)0.7000
B)0.5000
C)0.4615
D)0.1300

Accepted Answer

We need to find the probability of a patient having Medicare insurance given that they arrived by ambulance. This can be found using Bayes' theorem:

P(M | A) = (P(A | M) * P(M)) / P(A)

Where:
P(M | A) = Probability of having Medicare insurance given that the patient arrived by ambulance
P(A | M) = Probability of arriving by ambulance given that the patient has Medicare insurance (0.20)
P(M) = Probability of having Medicare insurance (0.30)
P(A) = Probability of arriving by ambulance (0.20*0.30 + 0.10*0.70 = 0.13)

Plugging in the values, we get:

P(M | A) = (0.20 * 0.30) / 0.13
P(M | A) = 0.4615

Therefore, the probability of a patient having Medicare insurance given that they arrived by ambulance is 0.4615, or approximately 46.15%. The best choice is C.

Question 4

Recently,a few companies have been accused of issuing stock options to their top executives at the lowest stock price of the year.Executives can later sell these stock shares at a higher price and make a large profit.In some companies,this happened several years in a row.An executive argued,"It's just a coincidence.There are about 250 trading days in a year,so there is a reasonable chance that my option price just happened to be lowest of the year." Discuss.

Accepted Answer

The answer of Recently,a few companies have been accused of...

Question 5

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)Cannot tell from given information

Accepted Answer

Collectively exhaustive events are events that cover all possible outcomes of an experiment. Therefore, the probability of one or the other event occurring is 1.00.

Question 6

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)0.7407
B)0.8000
C)0.5400
D)0.5000

Accepted Answer

P(N|C) = P(N) * P(C|N) / P(C)= 0.8 * 0.5 / (0.8 * 0.5 + 0.2 * 0.7)= 0.4 / 0.54= 0.7407

Question 7

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...

Question 8

From the following tree,find the probability that a randomly chosen person will get the flu vaccine and will also get the flu. 
A)0.10
B)0.07
C)0.19
D)0.70

Accepted Answer

To find the probability that a person will get the flu vaccine and get the flu, we need to find the probability of following path in the tree diagram: Flu vaccine -> Flu.
Looking at the diagram, we see that there are a total of 350 people and out of those, 70 got the vaccine and the flu (bottom right branch). Therefore, the probability of randomly choosing a person who got the vaccine and the flu is:
P(Flu vaccine and Flu) = 70/350 = 0.2
Therefore, the best choice is B, which is the closest to 0.2.

Question 9

Which best exemplifies the classical definition of probability?
A)The probability that a male age 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 of equally likely outcomes. Rolling a pair of dice is a classic example where each outcome (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12) is equally likely to occur, making it an appropriate example of the classical definition of probability. The other options do not meet the criteria of equally likely outcomes.

Question 10

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

The events are not independent because the probability of having an expired license is influenced by the probability of having an unpaid parking ticket, and vice versa. If they were independent, the probability of having both events would be the product of their individual probabilities, but in this case it is not (1% instead of 0.5%).

Question 11

From the following tree,find the probability that a randomly chosen person will not get a vaccination and will not get the flu. 
A)0.18
B)0.60
C)0.19
D)0.70

Accepted Answer

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

Question 12

Which best exemplifies a subjective probability?
A)The probability that a female age 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 on precise mathematical calculations or objective data. The probability that the summer Olympic games will be held in Chicago in 2020 is a subjective probability because it depends on various uncertain factors and personal beliefs or information available at the time the probability is assessed. Choices A, B, and D can be estimated using objective data or mathematical calculations, making them examples of objective probabilities.

Question 13

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 14

From the following tree,find the probability that a randomly chosen person will get the flu. 
A)0.19
B)0.07
C)0.81
D)0.70

Accepted Answer

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

Quiz 5: Probability

Which best exemplifies the empirical definition of probability?

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?

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

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

Which best exemplifies the classical definition of probability?

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 not get a vaccination and will not get the flu.

Which best exemplifies a subjective probability?

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.

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