Single Choice

If $$P(A\cup B)=\dfrac {2}{3}, P(A\cap B)=\dfrac {1}{6}$$ and $$P(A)=\dfrac {1}{3}$$, then

AA and B are independent events
Correct Answer
BA and b are disjoint events
CA and b are dependent events
DNone of these

Solution

If $$P(A\cup B)=\frac {2}{3}$$
$$P(A\cap B) = \frac {1}{6}$$
$$P(A)=\frac {1}{3}$$
$$P(A\cup B) = P(A) + P(B) - P(A\cap B)$$
$$\frac {2}{3} = \frac {1}{3} + P(B) - \frac {1}{6}$$
$$P(B) = \frac{1}{2}$$

Since, $$ P(A\cap B) = P(A).P(B)$$
Therefore, the events are independent.

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