Probability (P(A))

How to read it

OpenStax’s Contemporary Mathematics introduces P(E) as the number assigned to an event E, between 0 and 1 inclusive, with 0 for an impossible event and 1 for a certain one. When all the outcomes are equally likely, it is the number of outcomes in the event divided by the number of outcomes in the sample space, P(E) = n(E)/n(S). Grinstead and Snell’s Introduction to Probability (Dartmouth) gives the plainest example: for one roll of a fair die, the event F that a 6 comes up has P(F) = 1/6. The letter inside the brackets names an event, written as a capital letter like a set. Probabilities of an event and its opposite add to 1: OpenStax’s Introductory Statistics gives P(A) + P(A′) = 1, where A′ is the complement, everything that is not A.

Also searched as: P(A), P(E), P of A, Pr(A), probability notation, probability symbol.

P or Pr

Both are in use: Miller gives P(A) and Pr(A) as the two patterns, and Feller’s textbook used Pr. A small p on its own is something else in statistics, the P-value (p) of a test. Inside the brackets, set notation carries over: P(A ∪ B) is the probability of A or B, from the union, and P(A ∩ B) the probability of both, from the intersection.