If a call is sampled at random,the conditional probability that the call is not "6+" minutes long given that it is a long distance call is
A)120/300
B)10/300
C)0.9667
D)0.6667

Question

If a call is sampled at random,the conditional probability that the call is not "6+" minutes long given that it is a long distance call is 
A)120/300 
B)10/300 
C)0.9667 
D)0.6667

Quizplus · Accepted Answer

Let A be the event that the call is not "6+" minutes long and B be the event that it is a long distance call. We are given P(A|B)=0.9667. We know that P(A|B) = P(A∩B)/P(B). We are required to find P(A'|B). We have P(A'|B) = P(B∩A')/P(B) = [1- P(B∩A)]/P(B) = [1- P(A|B)*P(B)]/P(B) = [1- (0.9667*P(B))]/P(B). Since P(B)>=0, 0.9667<=P(A'|B)<=1. To get the maximum possible value of P(A'|B), we take P(B) = 1 which gives P(A'|B) = 1-0.9667 = 0.0333. Therefore, the best choice is C.

If a Call Is Sampled at Random,the Conditional Probability That