Question 5: If two events, A and B, are such that P(A) = .5, P(B) = .3, and P(A \cap B) = .1, find the following:
(a). P(A|B)
(b). P(B|A)
(c). P(A | (A \cup B))
(d). P(A | (A \cap B))
[Hint: A is a subset of (A \cup B); so A \cap (A \cup B) = A;]
[Hint: (A \cap B) is subset of A, so (A \cap B) \cap A = (A \cap B) ]
(e). P( (A \cap B) | (A \cup B)) [Hint: (A \cap B) is a subset of (A \cup B) ]
Hint: Final answers (a) 1/3, (b) 1/5, (c) 5/7, (d) 1, (e) 1/7. Please show details.