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 22 31 69 Humanities 7 60 40 Education 6 68 32 Social science 10 59 41 Natural sciences 6 50 50 Other 49 53 47

Explanation / Answer

Consider the table:

a)

From the table,

P(freshman and female) = 50.03% or 0.5003 [answer]

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b)

P(male) = 1 - P(freshman and female) = 0.4997 [answer]

**************

c)

P(business|female) = P(business and female) / P(female) = 0.1518/0.5003 = 0.303417949 [answer]

Major %freshman %male %female %freshman and male %freshman and female Business 22 31 69 6.82 15.18 Humanities 7 60 40 4.2 2.8 Education 6 68 32 4.08 1.92 Social science 10 59 41 5.9 4.1 Natural sciences 6 50 50 3 3 Other 49 53 47 25.97 23.03 Total 49.97 50.03

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