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.) Major % of Freshmen Choosing This Major % of Major That Is Female % of Major That Is Male Business 23 39 61 Humanities 10 58 42 Education 8 63 37 Social science 5 60 40 Natural sciences 10 56 44 Other 44 48 52 (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?

Answer 1

Answer:

a) 0.4953; b) 0.61; c) 0.181

Step-by-step explanation:

For part a,

We multiply the percentage of students in each major by the percentage of them that are female.  We then add these together:

0.23(0.39)+0.10(0.58)+0.08(0.63)+0.05(0.60)+0.10(0.56)+0.44(0.48) = 0.4953.

For part b,

We are looking strictly at the percentage of business students that are males.  Out of the business majors, 61% are male; this makes the answer for part b 0.61.

For part c,

The percentage of female students is 0.4953.  Out of these, 0.23(0.39) = 0.0897 are female.  This gives us

0.0897/0.4953 = 0.181.