The rule of subtraction follows directly from two important properties of probability:
- The probability of a sample point ranges from 0 to 1.
- The sum of probabilities of all the sample points in a sample space equals 1.
Rule of Subtraction The probability that event A will occur is equal to 1 minus the probability that event A will not occur.
P(A) = 1 – P(A’)
What does that mean?
So if you’ve got 4 A’s and 1 B and one spot to fill. The probability of all the sample letters (sum) is set at 1. The probability of pulling an A is 4/5 or 0.8 and pulling a B is 1/5 or 0.2. I guess it’s pretty easy to say that 1-P(A) = 1-0.8 = 0.2 = P(B) in this example.
So far so good.