Data Sufficiency (DS) | Re: The probability that event A occurs is 0.5 and the probability that ev

=>Condition 1)
We call an event A and an event B independent if P(A∩B) = P(A)*P(B).
P(A∩B) = P(A)*P(B) = 0.5 * 0.7 = 0.35.
P(A∩BC) = P(A) - P(A∩B) = 0.5 – 0.35 = 0.15.
This is sufficient.

Condition 2)
1 – P(A∪B) = 0.15. It means P(A∪B) = 0.85.
P(A∪B) = P(A) + P(B) - P(A∩B) = 0.5 + 0.7 - P(A∩B) = 0.85.
Thus P(A∩B) = 0.15.
P(A∩B^C) = P(A) - P(A∩B) = 0.5 – 0.35 = 0.15.
This is also sufficient too.

Ans: D

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