Suppose that 30% of Austin residents in general support a particular ballot meas

Question

Suppose that 30% of Austin residents in general support a particular ballot measure, but 40% of men do. (Assume that 50% of Austin residents are men.) ( Write out each response in complete sentences; each response should be an explanation of the answer, and not just a numeric answer.)

a. What proportion of Austin residents are both male and support the ballot measure?

b. What proportion of Austin residents are either male or support the ballot measure (or both)?

c. What proportion of ballot measure proponents are male? (Hint: Bayes' Rule.)

Explanation / Answer

Let there are total 100 residents in Austin.since 50% are men, that means there are 50 men in Austin

30% support particular ballot measure so 30 out of 100 do. Also, 40% of 50 men ie 20 men support it

a) P(male and support ballot)=20/100=20%

b) P(male or support ballot)=P(male)+P(support)-P(male and support)= 0.5+0.3-0.2=0.6 =60%

c) P(support ballot / male)=P(male and support ballet)/P(male) =20/50=40%

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