FInite Math (20 Questions)

QUESTION 1

The probability that a battery will last 10 hr or more is .75, and the probability that it will last 29 hr or more is .18. Given that a battery has lasted 10 hr, find the probability that it will last 29 hr or more.

​a.0.205

b.0.22

c.0.24

d.0.225

1 points   

QUESTION 2

A pair of fair dice is cast. Let E denote the event that the number landing uppermost on the first die is a 6 and let F denote the event that the sum of the numbers falling uppermost is 8. Determine whether E and F are independent events.
a.dependent

b.independent

1 points   

QUESTION 3

The proprietor of Cunningham's Hardware Store has decided to install floodlights on the premises as a measure against vandalism and theft. If the probability is 0.1 that a certain brand of floodlight will burn out within a year, find the minimum number of floodlights that must be installed to ensure that the probability that at least one of them will remain functional within the year is at least 0.999. (Assume that the floodlights operate independently.)
a.100

b.4

c.2

d.11

e.3

1 points   

QUESTION 4

An automobile manufacturer obtains the microprocessor used to regulate fuel consumption in its automobiles from three microelectronic firms: A, B, and C. The quality-control department of the company has determined that 1.5% of the microprocessors produced by firm A are defective, 1% of those produced by firm B are defective, and 2% of those produced by the firm C are defective. Firms A, B, and C supply 40%, 30%, and 30%, respectively, of the microprocessors used by the company. What is the probability that a randomly selected automobile manufactured by the company will have a defective microprocessor?
a.0.01000

b.0.01500

c.0.00700

d.0.02000

e.0.02200

1 points   

QUESTION 5

Let A and B be events in a sample space S such that and . Find: .

​a.

b.

c.

d.

1 points   

QUESTION 6

A tax specialist has estimated the probability that a tax return selected at random will be audited is .02. Furthermore, he estimates the probability that an audited return will result in additional assessments being levied on the taxpayer is .60.

What is the probability that a tax return selected at random will result in additional assessments being levied on the taxpayer?
a.0.037

b.0.038

c.0.012

d.0.022

1 points   

QUESTION 7

A pair of fair dice is cast. Let E denote the event that the number falling uppermost in the first die is 1 and let F denote the event that the sum of the numbers falling uppermost is 5.

Compute . Are E and F dependent events?
a., yes

b., yes

c., no

d., no

1 points   

QUESTION 8

Determine whether the given events A and B are independent. , , and .
a.independent

b.not independent

1 points   

QUESTION 9

A card is drawn from a well-shuffled deck of 52 playing cards. Let E denote the event that the card drawn is red and let F denote the event that the card drawn is a hearts. Determine whether E and F are independent events.
a.independent

b.not independent

1 points   

QUESTION 10

Determine whether the given events A and B are independent. , , and .​

a.dependent

b.independent

Two

QUESTION 1

The probability that a battery will last 10 hr or more is .75, and the probability that it will last 29 hr or more is .18. Given that a battery has lasted 10 hr, find the probability that it will last 29 hr or more.

​a.0.205

b.0.22

c.0.24

d.0.225

1 points   

QUESTION 2

A pair of fair dice is cast. Let E denote the event that the number landing uppermost on the first die is a 6 and let F denote the event that the sum of the numbers falling uppermost is 8. Determine whether E and F are independent events.

a.dependent

b.independent

1 points   

QUESTION 3

The proprietor of Cunningham's Hardware Store has decided to install floodlights on the premises as a measure against vandalism and theft. If the probability is 0.1 that a certain brand of floodlight will burn out within a year, find the minimum number of floodlights that must be installed to ensure that the probability that at least one of them will remain functional within the year is at least 0.999. (Assume that the floodlights operate independently.)
 

a.100

b.4

c.2

d.11

e.3

1 points   

QUESTION 4

An automobile manufacturer obtains the microprocessor used to regulate fuel consumption in its automobiles from three microelectronic firms: A, B, and C. The quality-control department of the company has determined that 1.5% of the microprocessors produced by firm A are defective, 1% of those produced by firm B are defective, and 2% of those produced by the firm C are defective. Firms A, B, and C supply 40%, 30%, and 30%, respectively, of the microprocessors used by the company. What is the probability that a randomly selected automobile manufactured by the company will have a defective microprocessor?
a.0.01000

b.0.01500

c.0.00700

d.0.02000

e.0.02200

1 points   

QUESTION 5

Let A and B be events in a sample space S such that and . Find: .

​a.

b.

c.

d.

1 points   

QUESTION 6

A tax specialist has estimated the probability that a tax return selected at random will be audited is .02. Furthermore, he estimates the probability that an audited return will result in additional assessments being levied on the taxpayer is .60.

What is the probability that a tax return selected at random will result in additional assessments being levied on the taxpayer?
 

a.0.037

b.0.038

c.0.012

d.0.022

1 points   

QUESTION 7

A pair of fair dice is cast. Let E denote the event that the number falling uppermost in the first die is 1 and let F denote the event that the sum of the numbers falling uppermost is 5.

Compute . Are E and F dependent events?
a., yes

b., yes

c., no

d., no

1 points   

QUESTION 8

Determine whether the given events A and B are independent. , , and .

a.independent

b.not independent

1 points   

QUESTION 9

A card is drawn from a well-shuffled deck of 52 playing cards. Let E denote the event that the card drawn is red and let F denote the event that the card drawn is a hearts. Determine whether E and F are independent events.

a.independent

b.not independent

1 points   

QUESTION 10

Determine whether the given events A and B are independent. , , and .​

a.dependent

b.independent