ProbabilityHard
Question
A and B are two independent events. The probability that A and B happen simultaneously is 
and neither A nor B happens is 
, then which of the following are true :
and neither A nor B happens is , then which of the following are true :Options
A.P(A) = 1/3, P(B) = 1/4
B.P(A) = 1/2, P(B) = 1/6
C.P(A) = 1/4, P(B) = 1/3
D.P(A) = 1/6, P(B) = 1/2
Solution
P(A ∩ B) = P(A) . P(B) = 
......(i)
= P
. P
= 
⇒ (1 - P(A)) (1 - P(B)) =
⇒ 1 - P(A) – P(B) + P(A) P(B) =
⇒ 1 - P(A) – P(B) +
= 
⇒ P(A) + P(B) =
.......(ii)
Solving (i) and (ii) gives P(A) =
Accordingly, P(B) =
......(i) = P . P = ⇒ (1 - P(A)) (1 - P(B)) =
⇒ 1 - P(A) – P(B) + P(A) P(B) =
⇒ 1 - P(A) – P(B) +
= ⇒ P(A) + P(B) =
.......(ii)Solving (i) and (ii) gives P(A) =
Accordingly, P(B) =
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