Skip to content

Rules of Probability

  • Lesson
  • 3 min read
  • 2 of 7 in this chapter

Basic Rules of Probability

  • The probability of any event is a number between 0 and 1.
  • All possible outcomes together must have probabilities that add up to 1.
  • If all outcomes in the sample space are equally likely, the probability that event A occurs can be found using the formula P(A) = (number of total outcomes corresponding to event A)/(total number of outcomes in sample space) Note: This only works if all the outcomes in the sample space are equally likely.
  • The probability that an event does not occur is 1 minus the probability that it does occur. We refer to the event “not A” as the complement of A and denote it by Ac.
  • If two events have no outcomes in common, the probability that one or the other occurs is the sum of their individual probabilities. When two events have no outcomes in common, we refer to them as mutually exclusive or disjoint. That is, P(A and B) = 0.

Basic Probability Rules (in symbols):

  • For any event A, 0 ≤ P(A) ≤ 1.
  • If S is the sample space in a probability model, P(S) = 1.
  • In the case of equally likely outcomes, P(A) = (number of outcomes corresponding to event A)/(total number of outcomes in sample space)
  • Complement rule: P(AC) = 1 - P(A).
  • Addition rule for mutually exclusive events: If A and B are mutually exclusive, P(A or B) = P(A) + P(B).

Important notes The use of the word “or” in probability questions is different from that in everyday life. In life, it usually means one or the other (“I’ll either go to the study session or go to a movie.”) In statistics, “A or B” could mean one or the other or both.

We can’t use the addition rule for mutually exclusive events unless two events have no outcomes in common. If A and B are not mutually exclusive, they can occur together. The probability that one or the other occurs is then less than the sum of their probabilities. That way, we don’t double count the outcomes that are common to both.

The General Addition Rule fixes overlap on events occurring together: P(A or B) = P(A) + P (B) - P(A and B). Subtracting the P(A and B) removes the overlap when adding probabilities.

In statistics, certain symbols denote and/or in probability. ⋃ = union, means or and ⋂ = intersection, means and. P(A⋃B) = P(A or B) P(A⋂B) = P(A and B)

image