1) The IRS says (I am making up this scenario) that 5% of the population cheat o
ID: 2933096 • Letter: 1
Question
1)
The IRS says (I am making up this scenario) that 5% of the population cheat on the income taxes every year and the result is independent of age, ethnicity, and income bracket; let us say this number holds for every year. Suppose that 40% of the population that filed income taxes is between the ages of 18 to 44 years for the year 2010. What is the probability that an adult that filed income taxes for the year 2010 cheated on their income tax and is between the ages of 18 to 44 years?
2)
The IRS says (I am making up this scenario) that 5% of the population cheat on the income taxes every year and the result is independent of age, ethnicity, and income bracket; let us say this number holds for every year. Suppose that 40% of the population that filed income taxes is between the ages of 18 to 44 years for the year 2010. Suppose we sampled five tax returns completely at random for the year 2010. What is the probability that at least one person is between the ages of 18 to 44 years of age?
3)
The IRS says (I am making up this scenario) that 5% of the population cheat on the income taxes every year and the result is independent of age, ethnicity, and income bracket; let us say this number holds for every year. Suppose that 40% of the population that filed income taxes is between the ages of 18 to 44 years for the year 2010.
Suppose we sampled three tax returns completely at random for the year 2010. What is the probability that at all three cheated on their income tax?
Explanation / Answer
1) probability that an adult that filed income taxes for the year 2010 cheated on their income tax and is between the ages of 18 to 44 years =0.4 *0.05 =0.02
2) probability of not being fromages of 18 to 44 years of age =1-0.4 =0.6
probabilty that at least one person is between the ages of 18 to 44 years of age =1-P( none of them are between the ages of 18 to 44 years of age)= 1-(0.6)5 =0.9222
3)
probabilty of cheating =0.05
hence probability that at all three cheated on their income tax =(0.05)3 =0.000125
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