The chances of a tax return being audited are about 21 in 1000 if an income is l

Question

The chances of a tax return being audited are about 21 in 1000 if an income is less than $100,000 and 40 in 1000 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 be audited? With income of $100,000 or more? Upper P left parenthesis taxpayer with income less than $ 100 comma 000 is audited right parenthesisequals nothing (Type an integer or a decimal.)

What is the probability that a taxpayer with income of $100,000 or more will be audited? Upper P left parenthesis taxpayer with income of $ 100000 or higher is audited right parenthesisequals nothing (Type an integer or a decimal.)

b. If four taxpayers with incomes under $100,000 are randomly selected, what is the probability that exactly one will be audited? That more than one will be audited? Upper P left parenthesis x equals 1 right parenthesisequals nothing (Round to four decimal places as needed.)

What is the probability that more than one will be audited? Upper P left parenthesis x greater than 1 right parenthesisequals nothing (Round to four decimal places as needed.)

c. Repeat part b assuming that four taxpayers with incomes of $100,000 or more are randomly selected. Upper P left parenthesis x equals 1 right parenthesisequals nothing (Round to four decimal places as needed.) What is the probability that more than one will be audited? Upper P left parenthesis x greater than 1 right parenthesisequals nothing (Round to four decimal places as needed.) d. If two taxpayers with incomes under $100,000 are randomly selected and two with incomes more than $100,000 are randomly selected, what is the probability that none of these taxpayers will be audited? P(none of the taxpayers will be audited)equals nothing (Round to four decimal places as needed.)

e. What assumptions did you have to make in order to answer these questions? A. We must assume that the variables are binomial random variables. We must assume that the trials are identical, the probability of success is the same from trial to trial, 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, the probability of success varies from trial to trial, and that the trials are dependent. C. We must assume that the variables are binomial random variables. We must assume that the trials are identical and dependent. D. We must assume that the variables are random variables. We must assume that the trials are identical, and the probability of success varies from trial to trial.

Explanation / Answer

answer:

(a)

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