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t View History Bookmarks Window Help % www webas sign, net/web Studrnt 21 Math 141 ect. 7-6 The Office of Admissions (Round your answers to three declmal places.) and Records of a large western unlversity released the accompanying information concerning the majors of its freshman class. % of Freshmen % of Major That Is Female % of Major That Is Male Major BusinesS Humanities Educat Social science Natural sciences This Major 39 38 62 51 43 53 (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? (e) What is the probability that a female student selected at random from the freshman class is majoring in business? O -125 points TEAFMAC2 1.7 026. 0/6 Submissions Used Tree machines turn out all the products in a factory, with the first machine producing 15% of the products, the second machine 35%, and the third machine 50% The

Solution

a)According to given probelm total students=100(28+6+8+8+6+44)

the probability that a student selected at random from the fresman class is a female is

P(F)=(28/100)*(0.32)+(6/100)*(0.61)+(8/100)*(0.62)+(8/100)*(0.51)+(6/100)*(0.57)+(44/100)*(0.47)

      =(0.28)*(0.32)+(0.06)*(0.61)+(0.08)*(0.62)+(0.08)*(0.51)+(0.06)*(0.57)+(0.44)*(0.47)

      =0.0896+0.0366+0.0496+0.0408+0.0342+0.2068

      =0.4576

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

      P(B/M)=[P(B)P(M/B)]/P(M)

now P(M)=(28/100)*(0.68)+(6/100)*(0.39)+(8/100)*(0.38)+(8/100)*(0.49)+(6/100)*(0.43)+(44/100)*(0.53)

             =(0.28)*(0.68)+(0.06)*(0.39)+(0.08)*(0.38)+(0.08)*(0.49)+(0.06)*(0.43)+(0.44)*(0.53)

            =0.1904+0.0234+0.0304+0.0392+0.0258+0.2332

            =0.5424

then P(B/M)=[P(B)P(M/B)]/P(M)

                  =[(28/100)*(0.68)]/[(28/100)*(0.68)+(6/100)*(0.39)+(8/100)*(0.38)+(8/100)*(0.49)+(6/100)*(0.43)+      (44/100)*(0.53)]

                   =[(0.28)*(0.68)]/[0.5424]

                   =(0.1904)/(0.5424)

                   =0.3510

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

                P(B/F)=[P(B)P(F/B)]/P(F)

                         =[(28/100)*(0.32)]/[0.4576]      [from a]
                         =[(0.28)*(0.32)]/[0.4576]

                         =[0.0896]/[0.4576]

                         =0.1958