Answer to Question #238263 in Statistics and Probability for Kim

Question

20% of students in a class go to professor during office hours. of those who go 30% seek minor clarification. 70% seek major clarification. a) what is the probability a student goes for minor clarification? b) what is the probability a student goes for major clarification? 

Answer 1

Let A be the event that students go to professor and B the event that minor clarifications are sought. B^C is the event that major clarifications are sought.

The information in this question can be summarized as follows,

P(A)=0.2

P(B|A)=0.3

P(B^C|A)=0.7

To determine P(B), the property P(B^C AND A)= P(B^C)-P(B AND A) is applied, then obtain P(B)=1-P(B^C).

P(A AND B)=P(B AND A)=P(B|A)*P(A)

=0.3*0.2

=0.06

P(B^C AND A)=P(A AND B^C)=P(B^C|A)*P(A)

=0.7*0.2

=0.14

Therefore, we have

0.14=P(B^C)-0.06

P(B^C)=0.2, hence P(B)=1-0.2=0.8

a.

We find P(A|B)=P(A AND B)/P(B)

=0.06/0.8

=6/80

=3/40

b.

We find P(A|B^C)=P(A AND B^C)/P(B^C)

=0.14/0.2

=7/10