The result of tossing a coin once will be either head or tail. Let A and B be the events of observing head and tail, respectively. The events A and B are

Question 1 of 20

1.0 Points

The result of tossing a coin once will be either head or tail. Let A and B be the events of observing head and tail, respectively. The events A and B are:

 

 

  A.mutually exclusive

 

  B.independent

 

  C.conditional

 

  D.unilateral

 

 

Question 2 of 20

1.0 Points

The formal way to revise probabilities based on new information is to use:

 

 

  A.unilateral probabilities

 

  B.common sense probabilities

 

  C.conditional probabilities

 

  D.complementary probabilities

 

 

Question 3 of 20

1.0 Points

If 25 tickets are sold and 2 prizes are to be awarded, find the probability that one person will win both prizes if that person buys exactly 2 tickets.

 

 

  A.1/300

 

  B.1/700

 

  C.1/600

 

  D.1/2300

 

 

Question 4 of 20

1.0 Points

If a die is rolled one time, find the probability of getting a number greater than 2.

 

 

  A.2

 

  B.-1

 

  C.5/6

 

  D.4/6

 

 

Question 5 of 20

1.0 Points

If two events are mutually exclusive, what is the probability that both occur at the same time?

 

 

  A.0.00

 

  B.1.00

 

  C.0.50

 

  D.Cannot be determined from the information given.

 

 

Part 2 of 6 -

 

Question 6 of 20

1.0 Points

We assume that the outcomes of successive trials in a binomial experiment are:

 

 

  A.identical from trial to trial

 

  B.random numbers between 0 and 1

 

  C.probabilistically independent

 

  D.probabilistically dependent

 

 

Question 7 of 20

1.0 Points

Find the variance of the following probability distribution. 

X

P(X)

1

0.10

2

0.20

3

0.35

4

0.30

5

0.05

 

 

 

  A.1.1

 

  B.1.21

 

  C.1.05

 

  D.1.02

 

 

Question 8 of 20

1.0 Points

A die is rolled 360 times. Find the standard deviation for the number of 3s that will be rolled.

 

 

  A.60

 

  B.50

 

  C.7.1

 

  D.5.9

 

 

Question 9 of 20

1.0 Points

Suppose that 50 identical batteries are being tested. After 8 hours of continuous use, assume that a given battery is still operating with a probability of 0.70 and has failed with a probability of 0.30. 

What is the probability that between 25 and 30 batteries (inclusive) will last at least 8 hours?

 

 

  A.0.0839

 

  B.0.7792

 

  C.0.1186

 

  D.0.9169

 

 

Question 10 of 20

1.0 Points

If a gambler rolls two dice and gets a sum of 10, he wins $10, and if he gets a sum of three, he wins $20. The cost to play the game is $5. What is the expectation of this game?

 

 

  A.$3.06

 

  B.-$2.78

 

  C.-$3.06

 

  D.$2.78

 

 

Part 3 of 6 -

 

Question 11 of 20

1.0 Points

 

 

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

The annual returns, in percentages, on stocks A and B for three possible states of the economy are given in the table below.

 

Economy State

Probability

StockA

StockB

Good

0.5

40

20

Average

0.3

20

40

Bad

0.2

10

8


If one invested in StockA, what would be the expected annual percentage return? Place your answer, in percent, in the blank. For example, an expected 10 percent return would be recorded as 10. Do not use a percent sign.    

Question 12 of 20

1.0 Points

 

 

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

Find the mean of the probability distribution:

X

0

1

2

3

4

P(X)

0.12

0.16

0.24

0.30

0.18


Round your answer to two decimal place as necessary. For example, 4.56 would be a legitimate entry.

Mean =      

Question 13 of 20

1.0 Points

 

 

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

The following data were obtained from a survey of college students. The variable X represents the number of non-assigned books read during the past six months. 

x

0

1

2

3

4

5

6

P (X=x)

0.55

0.15

0.10

0.10

0.04

0.03

0.03


What is the variance of X?  Place your answer, rounded to two decimal places in the blank. For example, 4.56 would be a legitimate entry.

Question 14 of 20

1.0 Points

 

 

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

Find the expected value of the following probability distribution.

X

1

2

3

4

5

P(X)

0.05

0.20

0.35

0.25

0.15


Round your answer to two decimal place as necessary. For example, 4.56 would be a legitimate entry. 

Expected value =       

Part 4 of 6 -

 

Question 15 of 20

1.0 Points

 

 

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

Mothers Against Drunk Driving (MADD) is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Five hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:

                                                        Number of Vehicles Involved

Did alcohol play a role?

1

2

3

 

Yes

60

110

30

200

No

40

215

45

300

 

100

325

75

 

 

What proportion of accidents involved alcohol and a single vehicle?

Place your answer, rounded to 2 decimal places, in the blank. For example, 0.23 is a legitimate entry.  

Question 16 of 20

1.0 Points

 

 

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

The president of a bank is attempting to arrange a meeting with the three vice presidents for a Friday weekly meeting. He believes that each of these three busy individuals, independently of the others, has about 40% chance of being able to attend the meeting. What is the probability that at least two of the three vice presidents can attend the meeting? Place your answer, rounded to 3 decimal places, in the blank. For example, 0.123 would be a legitimate entry.  

Question 17 of 20

1.0 Points

 

 

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

In Major League Baseball there are five teams in the Western Division of the National League: Arizona, Los Angeles, San Francisco, San Diego, and Colorado. How many different orders of finish are there for these five teams? Place your answer in the blank. Do not use any decimal places or commas. For example, 45 would be a legitimate entry.  

Question 18 of 20

1.0 Points

 

 

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. 
Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. 
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. 

Mothers Against Drunk Driving (MADD) is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Five hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:

                                                         Number of Vehicles Involved

Did alcohol play a role?

1

2

3

 

Yes

60

110

30

200

No

40

215

45

300

 

100

325

75

 

 

Given that multiple vehicles were involved, what proportion of accidents involved alcohol?

 

Place your answer, rounded to 2 decimal places, in the blank. For example, 0.23 is a legitimate entry.  

Part 5 of 6 -

 

Question 19 of 20

1.0 Points

If A and B are two independent events with P(A) = 0.20 and P(B) = 0.60, then P(A and B) = 0.80

 

 

  True

  False

 

Part 6 of 6 -

 

Question 20 of 20

1.0 Points

The variance of a binomial distribution for which n = 50 and p = 0.20 is 8.0.

 

 

  True

  False

 

 

 
 

            

 
 
 

 

  • Posted: 4 years ago
Let A and B be the events of observing head and tail, respectively. The events A and B are

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