A and B are mutually exclusive events with P(B) = 0.25 and P(A ̅) = 0.4
Determine:
3.1 P(A∪B)
3.2 P(A ̅∪B)
3.3 P(A ̅ | B ̅)
3.1 P(A∪B) = P(A) + P(B) since A and B are mutually exclusive events
P(A∪B) = P(A) + P(B) = P(A ̅) + P(B) = 0.4 + 0.25 = 0.65
3.2 P(A ̅∪B) = P(A ̅) + P(B) - P(A ̅∩B)
As A and B are mutually exclusive events, P(A ̅∩B) = 0
Therefore, P(A ̅∪B) = P(A ̅) + P(B) = 0.4 + 0.25 = 0.65
3.3 P(A ̅ | B ̅) = P(A ̅∩B ̅) / P(B ̅)
As A and B are mutually exclusive events, P(A∩B) = 0
Therefore, P(A ̅∪B ̅) = P(A ̅) + P(B ̅) = P(A ̅) = 0.4
So, P(A ̅ | B ̅) = P(A ̅) / P(B ̅) = 0.4 / (1 - P(B)) = 0.4 / 0.75 = 0.5333 or 53.33%