Answer:
Case(a):
Case(b):
Case(c):
Step-by-step explanation:
Given
(a) events a and b are a partition and p[a] = 3p[b].
(b) for events a and b, p[a ∪ b] = p[a] and p[a ∩ b] = 0.
(c) for events a and b, p[a ∪ b] = p[a]− p[b].
we have to find the p[b] in each case:
Case (a): events a and b are a partition and p[a] = 3p[b].
gives
Case (b): for events a and b, p[a ∪ b] = p[a] and p[a ∩ b] = 0.
⇒
⇒
∵ p[a ∩ b] = 0.
Case(3): for events a and b, p[a ∪ b] = p[a]− p[b].
p[a ∪ b] = p[a]− p[b]
⇒
⇒
⇒