JEE Main | 2014Trigonometric EquationHard
Question
Let A and B be two events such that 
= 
, P(A ∩ B) = 
and P(
) = , where stands for the complement of the event A. Then the events A and B are
= , P(A ∩ B) = and P() = , where stands for the complement of the event A. Then the events A and B areOptions
A.Independent but not equally likely
B.Independent and equally likely
C.Mutually exclusive and independent
D.Equally likely but not independent
Solution
= 
⇒ P(A ∪ B) = 1- 
P(
) = 
⇒ P(A) = 1 - 
∵ P(A ∪ B) = P(A)+ P(B) - P(A ∩ B)
+ P(B) - 
P(B) =
∵ P(A) ≠ P(B) so they are not equally likely.
Also P(A) × P(B)
= P(A ∩ B)
∵ P(A ∩ B) = P(A).P(B) so A & B are independent.
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