Math miscellaneousHard
Question
A fair coin is tossed four times. If A is the event that a head occurs on each of the first three tosses, B is the event that a tail occurs in fourth toss and C is the event that exactly two heads occur in the four tosses, then the events -
Options
A.A and B are independent
B.B and C are independent
C.C and A are independent
D.A,B,C are independent
Solution
P(A) = 
, P(B) = 
P(C) = 
P(A ∩ C) =
P(C ∩ A) = 0, P(A ∩ B ∩ C) = 0
P(A ∩ B) = P(A)P(B), P(C ∩ A) ≠ P(C)P(A),
P(B ∩ C) = P(B) P(C))
⇒ A,B,C are not pair wise independent
⇒ A,B,C are not independent.
, P(B) = P(C) = P(A ∩ C) =
P(C ∩ A) = 0, P(A ∩ B ∩ C) = 0
P(A ∩ B) = P(A)P(B), P(C ∩ A) ≠ P(C)P(A),
P(B ∩ C) = P(B) P(C))
⇒ A,B,C are not pair wise independent
⇒ A,B,C are not independent.
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