Query on bayes theorem


#1

Let P(E) denote the probability of the occurrence of event E.
If P(A) = 0.5 and P(B) = 1, then the values of P(A/B) and P(B/A) respectively are

A)0.5, 0.25
B)0.25, 0.5
C)0.5, 1
D)1,0.5


#2

C. 0.5,1. Since both the events will occur the probability is P(A). i.e. P(A intersection B) = P(A).


#3

Since the P(B)=1 it means it is a sure event.

  1. Now probability of intersection of both events A and B, i.e., P(A∩B)=P(A)
  2. P(A|B) = P(A∩B)/P(B) = P(A)/P(B) = 0.5/1 = 0.5
  3. P(B|A) = P(A∩B)/P(A) = P(A)/P(A) = 0.5/0.5 = 1
    So the answer is option ‘c’.