Three events A, B and C have probabilities , respectively. Given that and , find the values of P (C | B) and P (A'∩ C').

Question

Three events A, B and C have probabilities , respectively. Given that and , find the values of P (C | B) and P (A' ∩ C').

Philoid · Accepted Answer

GIVEN THAT

AND,

AND

By De Morgan’s laws:

(A ∪ B)^’ = A^’∩ B^’
( A∩B)^’ = A^’∪ B^’

P (A'∩ C') = P(A Ս C)^’

= 1- P (A Ս C)

= 1-[P(A)+ P(C)- P (A Ո C)]