Let E1, E2, E3, …………. En mutually exclusive and exhaustive events and A is the event occurs after E1, E2, E3, …………. En.
By multiplication theorem,
, where i = 1, 2, 3, … n
Example 1: A man is known to speak truth 3 out of 4 times. He throws a die and reports it is a six. Find the probability that it is actually a six.
E1: Six comes up.
E2: Six does not comes up.
A: The man reports it is a six.
By Baye’s theorem, required probability is: