Define Independent events with examples.

1.	Define Independent events with examples.
Answer» 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 \(\frac{1}{2}\) = \(\frac{1}{4}\)

Answer»

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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