Question 36 of 55intermediate🔍 AnalyzeShort Answer2 marks
Check whether the following probabilities P(A) and P(B) are consistently defined (i) P(A) = 0.5, P(B) = 0.7, P(A ∩ B) = 0.6 (ii) P(A) = 0.5, P(B) = 0.4, P(A ∪ B) = 0.8
(i)
Answer
Not consistently defined
(ii)
Answer
Consistently defined
Explanation
This question tests the fundamental properties of probability. For probabilities to be consistently defined, they must satisfy: (1) P(A ∩ B) P(A) and P(A ∩ B) P(B), since intersection cannot exceed individual probabilities, and (2) the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B) must hold with all values between 0 and 1.