Question

5. A total of 20 percent of women and 25 percent of men who major in engineering are majoring in electrical engineering at LaGuardia Community College. The electrical engineering majors then transfer to the City College for completing their bachelors degree. If 85 percent of the engineering major are men, a. what percent of those electrical engineering majors transferring to City college are women? b. what percentage of the engineering majors will transfer to City college?

Answer 1

Here, we are given that: P( electrical | male ) = 0.25 and P( electrical | female ) = 0.20

Also, we are given that P( male ) = 0.85 and therefore P( female ) = 1 - 0.85 = 0.15

a) Using law of probability addition, we get here:

P( electrical ) = P( electrical | male ) P(male ) + P( electrical | female ) P( female )

P( electrical ) = 0.25*0.85 + 0.2*0.15 = 0.2425

Now using the bayes theorem, we get here:

P( women | electrical ) = P( electrical | female ) P( female ) / P( electrical )

P( women | electrical ) = 0.2*0.15 / 0.2425 = 0.1237

Therefore 0.1237 is the required probability here that is 12.37%

b) Only electrical majors transfer to the college. We computed above that:

P( electrical ) = 0.2425

Therefore 24.25% is the required answer here.