The chances of a tax return being audited are about 20in 1,000 if an income is less than$100,000 and 33 in 1,000if 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? What is the probability that a taxpayer with income of $100,000 or more will be audited?
b. If three 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?
P(x=1)=
What is the probability that more than one will be audited?
P(x>1)=
c. Repeat part b assuming that three taxpayers with incomes of $100,000 or more are randomly selected.
P(x=1)=
What is the probability that more than one will be audited?
P(x>1)=
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)=
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 random variables. We must assume that the trials are identical, and the probability of success varies from trial to trial.
D. We must assume that the variables are binomial random variables. We must assume that the trials are identical and dependent.