Survey results on the Age and Marital Status of women are given below. Use the d

Question

Survey results on the Age and Marital Status of women are given below. Use the data to answer the questions.

                                                       AGE

                      18 to 24       25 to 64       65 and over total

Married           3,046           48,116        7,767               58,929

Never Married 9,289             9,252           768               19,309

Widowed               19            2,425          8,636             11,080

Divorced             260            8,916          1,091              10,267

total               12,614            68,709        18,262             99,585

A. What is the probability of a randomly selected woman being Never Married?

B. What is the probability of a randomly selected woman being Married and 25 to 64?

C. What is the probability of a randomly selected woman being Married or 25 to 64?

D If a woman is 18 to 24 years of age, what is the probability that she is Divorced?

E. Are age and marital status independent events? Show your proof.

Assume that each year the IRS randomly audits 5% (0.05) of the tax returns. If a married couple has filed separate returns, what is the probability that: A. both the husband and the wife will be audited? B. either the husband or the wife will be audited?

Explanation / Answer

A. What is the probability of a randomly selected woman being Never Married?

total women who never married = 19309 , and total population = 99585

so the probability required is 19309/99585 = 0.1938

B. What is the probability of a randomly selected woman being Married and 25 to 64?

woman being Married and 25 to 64 = 48116

and total population = 99585

so the probability required is 48116/99585 = 0.483

C. What is the probability of a randomly selected woman being Married or 25 to 64?

total married women = 58,929 and total women in age 25-64 group = 68709

so required probability is (58929 + 68709-48116)/  99585 = 0.798 , we substract 48116 because thats already accounted for while considering the age group

D If a woman is 18 to 24 years of age, what is the probability that she is Divorced?

total women in this age group 12614

total divorced is 260

so the probability is 260/12614 = 0.0206

please note that we can answer only 4 subparts of a question at a time , as per the answering guidelines

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