Having a little troiuble understanding a and b, feel free to tackle c and d as w

Question

Having a little troiuble understanding a and b, feel free to tackle c and d as well. I understnad that for this question we should use bayes theorem: P(A|B) = P(A) * [ P (B|A) / P(B) ]. Any help would be appreciated!

Suppose that 30% of the men in California are Hispanic, and that 10% of Hispanic men have the first name Hector. One percent of non-Hispanic men are named Hector.

You receive an email from someone in California named Hector. What is the probability that he is Hispanic?

It turns out that you read the address wrong. Hector who sent you the email is in North Carolina, not California. In North Carolina, only 10% of men are Hispanic. What is the probability that Hector is Hispanic?

The Bertrand-Mullainathan experiment with CVs was conducted in Massachusetts and Chicago. The proportion of African-Americans is considerably higher in the Chicago area than it is in Massachusetts. If the results of the experiment are due to employer discrimination, how would the differences in name-response differ between Chicago and Massachusetts, if at all? Why or why not?

Suppose you found that there was no difference in employer response between Massachusetts and Chicago. What would you conclude?

Explanation / Answer

Hispanic Person name starting with Hector in california = 0.30*0.10 = 0.03

Non-Hispanic Person non starting with Hector in california = 0.70*0.01 = 0.007

The probablity that letter received is from Hispanic = 0.30*0.10 = 0.03

In North Carolina only 10% are hespanic but the percentage of men's name starting with hector is not mentioned hence we can calculate the probablity that the person is hispanic.

I found there would be non response from the employer end between Massachusetts and Chicago as the inforamation shared was only about the african-Americans which wont be any diffrence in the result as now a days name Hector is been used by all the nationals not only American's.

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