Question

Suppose that P(A)=1/2 and P(B)=1/3

1. Assume that A and B are neither independent nor disjoint, but that it is known that P(A|B)=1/4. Recalculate the probabilities listed.

a. P(A∩B):

b. P(A∪B):

c. P(A|B):

d.P(B|A):

Answer 1

a) P( A B) = P( A/B) * P( B)

P( A B) = (1/4)*(1/3)

P( A B) = 1/12

b) P( A U B) = P( A) + P( B) - P( A B)

P( A U B) = 1/2 + 1/3 - 1/12

P( A U B) = 3/4

c) P( A / B) = P( A B)/P( B) = 1/12/1/3

P( A / B) = 1/4

d) P( B/A) = P( A B)/P( A) = (1/12)/(1/2)

P( B /A) = 1/6