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  • If P (A ∪ B) = P (A ∩ B) for any two events A and B, then A. P (A) = P B. (B) P (A) > P (B) C. P (A) < P (B) D. none of these

If P (A ∪ B) = P (A ∩ B) for any two events A and B, then
A. P (A) = P
B. (B) P (A) > P (B)
C. P (A) < P (B)
D. none of these

Answers (1)

P (A ∩B) = P (A U B)

Now, P (A U B) = P (A) + P (B) – P (A ∩ B)        ……. (by general addition rule)

P (A ∩ B) = P (A) + P (B) – P (A ∩ B)       

Thus, [P (A) – P (A  ∩ B)] + [P (B) – P (A ∩ B)] = 0

Now,

P (A) – P (A  ∩ B) ≥ 0

& P (B) – P (A  ∩ B) ≥ 0

P (A) – P (A  ∩ B) = 0

P (B) – P (A  ∩ B) = 0

Thus, P (A) = P (A  ∩ B)

& P (B) = P (A  ∩ B)

Therefore, we get

P(A) = P (B)

Thus, option A is the correct answer.
 

Posted by

infoexpert22

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