1. Introduction to Probability & Statistics Expectations

2. Operational Rules Mutually Exclusive Events: P(A B) = P(A) + P(B) A

3. Conditional Probability
Now suppose we know that event A has occurred. What is the probability of B given A? A
A  B
P(B|A) = P(A  B)/P(A)

4. Example
Suppose for the same exponential distribution, we know the probability that the machine will last at least a more hrs given that it has already lasted c hrs. a c
c+a
Pr{X > a + c | X > c} = Pr{X > a + c  X > c} / Pr{X > c}
= Pr{X > a + c} / Pr{X > c}    e c a  ( )