If `P(A)=(2)/(3), P(B)=(1)/(2) " and " P(A cup B)=(5)/(6)`, then events A and B areA. mutually exclusiveB. independent as well as mutually exclusiveC. independentD. dependent only on A

If `P(A)=(2)/(3), P(B)=(1)/(2) " and " P(A cup B)=(5)/(6)`, then event

1.	If `P(A)=(2)/(3), P(B)=(1)/(2) " and " P(A cup B)=(5)/(6)`, then events A and B areA. mutually exclusiveB. independent as well as mutually exclusiveC. independentD. dependent only on A
Answer» Correct Answer - C We have, `P(A)=(2)/(3), P(B)=(1)/(2) " and " P(A cup B)=(5)/(6)` `therefore P(A cup B)=P(A)+P(B)-P(A cup B)` `implies P(A cup B)=(2)/(3)+(1)/(2)-(5)/(6)=(1)/(3)` Clearly, P(AB)=P(A)P(B) Hence, A and B are independent events. Since independent events are never mutually exclusive. So, option (c ) is correct.

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If `P(A)=(2)/(3), P(B)=(1)/(2) " and " P(A cup B)=(5)/(6)`, then events A and B areA. mutually exclusiveB. independent as well as mutually exclusiveC. independentD. dependent only on A

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