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’)
 
Fantastic.
 
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.