ProbabilityHard
Question
The probabilities of events, A ∩ B, A, B & A ∪ B are respectively in A.P. with second term equal to the common difference. Therefore A & B are:
Options
A.mutually exclusive
B.independent
C.such that one of them must occur
D.such that one is twice as likely as the other
Solution
P(A ∩ B) = a, P(A) = a + d, P(B) = a + 2d
P(A ∪ B) = a + 3d also a + d = d
⇒ a = 0
⇒ P (A ∩ B) = 0, P (A) = d , P (B) = 2d
P(A ∪ B) = 3d
P(A ∪ B) = a + 3d also a + d = d
⇒ a = 0
⇒ P (A ∩ B) = 0, P (A) = d , P (B) = 2d
P(A ∪ B) = 3d
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