Alt Ctrn 9. Assume that each year the IRS randomly audits 10% of the tax retums.
ID: 3366237 • Letter: A
Question
Alt Ctrn 9. Assume that each year the IRS randomly audits 10% of the tax retums. Ifa mamed couple has filed sopuane returns a. What is the probability that both the husband and the wife will be audited? b. What is the probability that only one of them will be audited e. What is the probability that neither one of them will be audited? d. What is the probability that at least one of them will be audited? Assume you are taking two courses this semester (A and B). The probability that you will pass course Ais 0.835, the probability that you will pass both courses is 0.276. The probability that you will pass at least one of the courses is 0.981 10. What is the probability that you will pass course B? Is the passing your answer Are the events of passing the courses mutually exclusive? Explain. a. b. of the two courses independent events? Use probability information to justify c. Short Answer Assume your favorite football team has 3 games left to finish the season. The outcome of each game can be win, lose, or tie. How many possible outcomes exist? 11.Explanation / Answer
Ans:
9)
a)P(both will be audited)=0.1*0.1=0.01
b)P(only one of them will be audited)=0.1*0.9+0.9*0.1=2*0.1*0.9=0.18
c)P(neither is audited)=0.9*0.9=0.81
b)P(atleast one of them is audited)=1-0.81=0.19
10)
Given that
P(A)=0.835
P(A and B)=0.276
P(atleast one)=P(A or B)=0.981
a)
P(A or B)=P(A)+P(B)-P(A and B)
0.981=0.835+P(B)-0.276
P(B)=0.981-0.835+0.276
P(B)=0.422
b)For two events to be independents,
P(A and B)=P(A)*P(B)
In above case,
P(A)*P(B)=0.835*0.422=0.352,which is not equal to P(A and B)=0.276
So,A and B are not independnet events.
c)For two events to be mutuall exclusive,
P(A and B)=0
But,in above case P(A and B)=0.276,so A and B are not mutually exclusive.
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