The chances of a tax return being audited are about 14 in 1,000 if an income is less than$100,000 and 38 in

1,000 if an income is$100,000 or more. Complete parts a through e.

a. What is the probability that a taxpayer with income less than$100,000 will beaudited? With income of$100,000 ormore?

Upper P left parenthesis taxpayer with income less than $ 100 comma 000 is audited right parenthesis

P(taxpayerwithincomelessthan$100,000isaudited)equals

=

What is the probability that a taxpayer with income of$100,000 or more will beaudited?

Upper P left parenthesis taxpayer with income of $ 100 comma 000 or higher is audited right parenthesis

P(taxpayerwithincomeof$100,000orhigherisaudited)equals

=

b. If four

four taxpayers with incomes under$100,000 are randomlyselected, what is the probability that exactly one will beaudited? That more than one will beaudited?

Upper P left parenthesis x equals 1 right parenthesis

P(x=1)equals

=

(Round to four decimal places asneeded.)

What is the probability that more than one will beaudited?

Upper P left parenthesis x greater than 1 right parenthesis

P(x>1)equals

=

(Round to four decimal places asneeded.)

c. Repeat part b assuming that four

four taxpayers with incomes of$100,000 or more are randomly selected.

Upper P left parenthesis x equals 1 right parenthesis

P(x=1)equals

=

(Round to four decimal places asneeded.)

What is the probability that more than one will beaudited?

Upper P left parenthesis x greater than 1 right parenthesis

P(x>1)equals

=

d. If two taxpayers with incomes under$100,000 are randomly selected and two with incomes more than$100,000 are randomlyselected, what is the probability that none of these taxpayers will beaudited?

P(none of the taxpayers will be audited)equals

=

e. What assumptions did you have to make in order to answer thesequestions?

A.

We must assume that the variables are binomial random variables. We must assume that the trials areidentical, the probability of success is the same from trial totrial, and that the trials are independent.

B.

We must assume that the variables are binomial random variables. We must assume that the trials are identical and dependent.

C.

We must assume that the variables are binomial random variables. We must assume that the trials areidentical, the probability of success varies from trial totrial, and that the trials are dependent.

D.

We must assume that the variables are random variables. We must assume that the trials areidentical, and the probability of success varies from trial to trial.