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Define Independent events with examples.

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Independent events: If the outcome of event A does not affect the outcome of event B, then the events A and B are called independent events. 

P ( A and B) = P(A). P(B)

Ex. Two dice are thrown. Find the probability of getting a prime number on one dice and even number on the other dice.

Here both the events are independent, so 

P ( a prime number) = \(\frac{3}{6}\) \(\frac{1}{2}\) (\(\therefore\) There are 3 prime numbers 2, 3, 5)

P ( an even number) =\(\frac{3}{6}\) = \(\frac{1}{2}\) (\(\therefore\) There are 3 even numbers 2, 4, 6)

\(\therefore\) Reqd. probability = \(\frac{1}{2}\) x \(\frac{1}{2}\) = \(\frac{1}{4}\) 

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