Trigonometric EquationHard
Question
Let A and B be two events such thatP 
and P 
where 
stands for complement of event A. Then events A and B are
and P where stands for complement of event A. Then events A and B areOptions
A.equally likely and mutually exclusive
B.equally likely but not independent
C.independent but not equally likely
D.mutually exclusive and independent
Solution
and 
⇒ P(A ∪ B) = 5/6 P(A) = 3/4
Also P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
⇒ P(B) = 5/6 - 3/4 + 1/4 = 1/3
P(A) P(B) = 3/4 - 1/3 = 1/4 = P(A ∩ B)
Hence A and B are independent but not equally likely.
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