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Question

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.


Solution

$$A=\{2,4,6\}$$
$$B=\{1,2,3\}$$
$$A\cap B=\{2\}$$
$$P(A\cap B)=1/6$$
$$P(A)=\cfrac12$$
$$P(B)=\cfrac12$$
$$P(A)P(B)=\cfrac14\ne P(A\cap B)$$
So $$A$$ and $$B$$ are independent events.

Mathematics

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