Q2 of 12 Page 13

A die, whose faces are marked 1, 2, 3, in red and 4, 5, 6 in green, is tossed. Let A be the event “number obtained is even” and B be the event “number obtained is red”. Find if A and B are independent events.[CBSE 2017]

Concept Used: Two events are said to be independent if one event in no way affects the other event. P(A ∩ B) ≠ P(A) P(B)

We have-

A = number obtained is even = {2, 4, 6}


B = number obtained is red = {1, 2, 3}


and


A ∩ B = {2}


Now,


P(A) = (3/6) = (1/2)


P(B) = (3/6) = (1/2)


and


P(A ∩ B) = (1/6)


Clearly, P(A ∩ B) ≠ P(A) P(B)


So, A and B are independent events.

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