19. The number of girls and boys enrolled for different majors in a community co

Question

19. The number of girls and boys enrolled for different majors in a community college are listed in the table below Major Girls Boys Total Biology 150 120 270 Sfats 110 130 240 Total 535 500 1035 a. If a student is chosen at random, what is the probability that the student is a boy? [Ans: 0.4830] Chemistry 100 100 200 Medicine 175 150 325 b. If a student is chosen at random, what is the probability that the student is a boy enrolled in stats? [Ans: 0.1256] c. What is the probability thot the student is a gin given that she is biology majore [Ans: 0.5555 d. what is the probobility that the student is biology mojor given that she is a gite (Ans: 0.2804 e. What is the probability thot the student selected is a biology major or stats major?(Ans:0.493 f. What is the probability that the student selected is a chemistry major or is a girl? (Ans: 0.614] g. What is the probability that the student selected is a girl and a medicine major? [Ans: 0.169] h. What is the probability that the student selected is a boy or a chemistry major? (Ans:0.58 © Venkateswara Rao Mudunuru Fall 2017 Exam-a Review Sheet

Explanation / Answer

n= total number of student in a community college = 1035

G= Total girls = 150+100+110+175= 535

B= Total girls = 120+100+130+150= 500

Bi= Total students in biolagy major = 150+120 = 270

Ch=Total students in chemistry major = 100+100 = 200

St = Total students in stats major = 110+130 = 240

Md =Total students in medicine major = 175 +150 = 325

Let's solve the all the part's

a)

Probability that student is boy = B/n = 500/1035 = 0.4830

b)

Probability that boy student is enroled in stats = number of boys in stats / n = 130 /1035 = 0.125603 (after rouding upto 4 decimal ) = 0.1256

c)

probability that student is girl given that she is biology major = number of girls in biolagy /Bi = 150/270 = 0.5555

d)

probability that the student is biology given that she is a girl = number of girls in biology / G = 150 / 535 = 0.28037

= 0.2804 (after rounding up to 4 decimal point )

e)

Probability that the selected student is biology major or stats major = (Bi/n) + (St/n) (we take addition because of the word ' or ' in between biology major 'or' stats major )  

  

= (270/1035) + (240/1035) = 0.49275(round upto 3 decimal point)

= 0.493

f)

Probability that the selected student is chemistry major or girls major = Ch/n + G/n - 100 / n

(we subtracted 100 because 100 girls are present in chemistry major and G also and it is counted twice i.e 100 in chemistry and 100 in G so we subtracted 100 )

= (200/1035) + (535/1035) - (100/1035)

= 0.61352(round it up to 3 decimal point )

= 0.614

g)

Probability that the selected student is a girl and a medicine major = girls in medicine major / n = 175 / 1035=0.169

h)

Probability that the selected student is a boy or a chemistry major = (B/n) + (Ch/n) - (100/n)

  we subtracted 100 because 100boys are present in chemistry major and B also and it is counted twice i.e 100 in chemistry and 100 in B so we subtracted 100 )   

= (500/1035)+(200/1035) -(100/1035) = 0.5797 (round it to up to 2 decimial point ) = 0.58

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