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	Freshmen Choosing      This Major, %	Females Choosing      This Major, %	Males Choosing      This Major, %
Business	21	31	69
Humanities	8	65	35
Education	10	64	36
Social science	7	59	41
Natural sciences	8	59	41
Other	46	46	54

(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

a)The probability that a student selected at random from the freshman class is a female:

P(F)=(0.21*0.31)+(0.08*0.65)+(0.10*0.64)+(0.07*0.59)+(0.08*0.59)+(0.46*0.46)
=0.4812

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

P(Male|Business)=P(Male and Business)/P(Business)

=(0.21*0.69)/0.21

=0.69

c) The probability that a female student selected at random from the freshman class is majoring in business:

P(B|F)=P(B n F)/P(F)

=(0.21*0.31)/0.4812

=0.1352

=