# If two events are independent, what is the probability that they both

Question 1 of 20

1.0 Points

If two events are independent, what is the probability that they both occur?

A.0.0

B.0.5

C.1.00

D.Cannot be determined from the information given Reset Selection

Question 2 of 20

1.0 Points

The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If a person is selected at random, what is the probability that he or she is a factory worker?

A.1/4

B.2/5

C.5/8

D.1/8 Reset Selection

Question 3 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.independent

B.unilateral

C.conditional

D.mutually exclusive Reset Selection

Question 4 of 20

1.0 Points

Sue has 10 pictures but only has space in her apartment to hang 4 of them on a wall. The number of different arrangements of four pictures from a selection of ten pictures is:

A.151,200

B.5,040

C.24

D.210 Reset Selection

Question 5 of 20

1.0 Points

What type of probability uses sample spaces to determine the numerical probability that an event will occur?

A.conditional probability

B.empirical probability

C.classical probability

D.subjective probability Reset Selection

Part 2 of 6 –

Question 6 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 greater than 40 batteries will last at least 8 hours?

A.0.0402

B.0.4538

C.0.9598

D.0.0789 Reset Selection

Question 7 of 20

1.0 Points

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

P (X=x)

0.20

0.25

0.20

0.15

0.10

0.10

Find P( X 5)

A.0.10

B.0.90

C.0.20

D.1.00 Reset Selection

Question 8 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 fewer than 40 batteries will last at least 8 hours?

A.0.7986

B.0.9211

C.0.9598

D.0.0789 Reset Selection

Question 9 of 20

1.0 Points

If a student randomly guesses at 20 multiple-choice questions, find the probability that the student gets exactly four correct. Each question has four possible choices.

A.0.19

B.0.17

C.0.08

D.0.23 Reset Selection

Question 10 of 20

1.0 Points

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

P (X=x)

0.20

0.25

0.20

0.15

0.10

0.10

What is the expected value of X?

A.3.65

B.6.25

C.2.0

D.1.20 Reset Selection

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 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

Find P(X 2). Place your answer, rounded to two decimal places in the blank. For example, 0.56 would be a legitimate entry.

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.

In February 2002 the Argentine peso lost 70% of its value compared to the United States dollar. This devaluation drastically raised the price of imported products. According to a survey conducted by AC Nielsen in April 2002, 68% of the consumers in Argentina were buying fewer products than before the devaluation, 24% were buying the same number of products, and 8% were buying more products. Furthermore, in a trend toward purchasing less-expensive brands, 88% indicated that they had changed the brands they purchased. Suppose the following complete set of results were reported. Use the following data to answer this question.

Number of Products Purchased

Brands Purchased

Fewer

Same

More

Total

Same

10

14

24

48

Changed

262

82

8

352

Total

272

96

32

400

What is the probability that a consumer selected at random purchased the same number or more products than before? Place your answer, rounded to 4 decimal places, in the blank.

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.

In February 2002 the Argentine peso lost 70% of its value compared to the United States dollar. This devaluation drastically raised the price of imported products. According to a survey conducted by AC Nielsen in April 2002, 68% of the consumers in Argentina were buying fewer products than before the devaluation, 24% were buying the same number of products, and 8% were buying more products. Furthermore, in a trend toward purchasing less-expensive brands, 88% indicated that they had changed the brands they purchased. Suppose the following complete set of results were reported. Use the following data to answer this question.

Number of Products Purchased

Brands Purchased

Fewer

Same

More

Total

Same

10

14

24

48

Changed

262

82

8

352

Total

272

96

32

400

What is the probability that a consumer selected at random purchased fewer products than before and changed brands? Place your answer, rounded to 4 decimal places, in the blank.

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 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 =

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.

At a certain college, there were 600 science majors, 200 engineering majors, and 500 business majors. If a student is selected at random, what is the probability that the student is an engineering major?

Place your answer, rounded to four decimal places, in the blank. When entering your answer do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 0.1234 would be 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.

A lock on a bank vault consists of three dials, each with 30 positions, In order for the vault to open, each of the three dials must be in the correct position. How many different “dial combinations” are there for this lock? Place your answer in the blank. Do not use any decimal places or commas. For example, 12345 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.

An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events:

= chocolate chosen

= strawberry chosen

= vanilla chosen

= ice cream on a cone

ice cream in a cup

Find the probability that the ice cream was sold in a cup and was vanilla flavor. Place your answer, rounded to 2 decimal places, in the blank. For exampe, 0.34 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.

An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events:

= chocolate chosen

= strawberry chosen

= vanilla chosen

= ice cream on a cone

ice cream in a cup

Find the probability that the ice cream was strawberry flavor, given that it was sold in a cup. Place your answer, rounded to 4 decimal places, in the blank. For exampe, 0.3456 would be a legitimate entry.

Part 5 of 6 –

Question 19 of 20

1.0 Points

Jim and Mike go to a coffee shop during their lunch break and toss a coin to see who will pay. The probability that Mike will pay three days in a row is 0.125.

True

False

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Part 6 of 6 –

Question 20 of 20

1.0 Points

If X is a binomial random variable with n = 20, and p = 0.30, then P(X = 10) = 0.50.

True

False

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