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 \(\frac{1}{2}\) = \(\frac{1}{4}\)