Question

Given p(a) = 1/4,p(b) = 1/3,p(a and b) = 1/2 evaluate p(a/b), p(b/a)

Answer 1

Answer: P(A/B) = 3/2  , P(B/A) = Invalid

Step-by-step explanation:

Given,

P(A) = 1/4

P(B) = 1/3

P(A∩B) = 1/2

P(A/B) = ?

P(B/A) = ?

We know  that,

P(A/B) = P(A∩B)/P(B)

P(A/B) = (1/2)/(1/3)

P(A/B) = 3/2

Also,

P(B/A) = P(A∩B)/P(A)

P(B/A) = (1/2)/(1/4)

P(B/A) = 4/2

P(B/A) = 2, Which is not possible,

Explanation:- We know  that P(B/A) denotes probability of  occurring event B while A has  already done. We know that probability can only be  less than of equal to 1. Hence, We can say that there is  not  chance of occurring event B while A has already done. For example, In a race if A  wins the match, then B cannot win the same match at same time