The Office of Admissions and Records of a large western university released the

Question

The Office of Admissions and Records of a large western university released the accompanying information concerning the contemplated majors of its freshman class. (Round your answers to three decimal places.)

(a) What is the probability that a student selected at random from the freshman class is a female?


(b) What is the probability that a business student selected at random from the freshman class is a male?


(c) What is the probability that a female student selected at random from the freshman class is majoring in business?

Major     % of Freshmen    
Choosing
This Major     % of Major    
That Is
Female     % of Major    
That Is
Male Business 26 38 62 Humanities 6 65 35 Education 5 61 39 Social science 10 54 46 Natural sciences 9 53 47 Other 44 48 52

Explanation / Answer

a) P(a student selected at random from the freshman class is a female) = 0.26x0.38 + 0.06x0.65 + 0.05x0.61 + 0.10x0.54 + 0.09x0.53 + 0.44x0.48

= 0.4812

b) P(business student selected at random from the freshman class is a male) = 1 - 0.4812 = 0.5188

c) P(a female student selected at random from the freshman class is majoring in business)

= P(a female student majoring in business)/P(females student)

= 0.26x0.38/0.4812

= 0.2053

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