+2 votes
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Fifty-two percent of the students at a certain college are females. Five percent
of the students in this college are majoring in computer science. Two percent of
the students are women majoring in computer science. If a student is selected at
random, find the conditional probability that
(a) this student is female, given that the student is majoring in computer science;
(b) this student is majoring in computer science, given that the student is
female.

How to solve this qn by growing tree method?
asked | 85 views
0
a) 0.02

b) 0.00192 ?
0
Answer is given in instructors manual is,

(a) P(F|CS) = P (F,CS) / P(CS)
= .02 / .05
= 2/5
(b) P(CS|F) = P(F,CS) / P(F)
= .02 /.52
= 1/26

1 Answer

0 votes
let event F represents that the selected student is female,M represents that selected student is male,R represents that selected female student is majoring in computer science,S represents that selected male student is majoring in computer science.
so P(F)=0.52
P(M)=0.48
let total student is 100.so 52 students are female and 2 among them are majoring in computer science.
so,P(R/F)=2/52
let total student is 100.so 5 students are majoring in computer science in total and 2 female students are majoring in computer science.so(5-2)=3 male students are majoring in computer science .And total male students=(100-52)=48
so,P(S/M)=3/48
for a,we have to evaluate P(student is female/student is majoring in computer science )=
(P(F)*P(R/F)) / ((P(F)*P(R/F) )+(P(M)*P(S/M) )
=(2/52 * 0.52) / ((2/52 * 0.52) + (0.48 *  3/48))
=0.4

for b,we have to evaluate P(student is majoring in computer science/student is female )=P(R/F)=2/52
answered by Active (4.2k points)
edited

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