Question:
Three events A, B and C have probabilities 2/5, 1/3 and ½ respectively. Given that P(AÇ C) = 1/5 and P(B Ç C) = ¼, find the values of P(C | B) and P(A’Ç C’).
Solution:
Given, P(A) = 2/5, P(B) = 1/3 and P(C) = ½
P(A Ç C) = 1/5 and P(B Ç C) = ¼
So, P(C/B) = P(B Ç C)/ P(B) = (¼)/ (1/3) = ¾
P(A’ Ç C’) = 1 – P(A ⋃ C)
= 1 – [P(A) + P(C) – P(A Ç C)]
= 1 – [2/5 + ½ – 1/5] = 1 – 7/10 = 3/10
Therefore, the required probabilities are ¾ and 3/10.