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Law of Total Probability P(A+B)

P(A+B)=P(A)+P(B)-P(A,B)
Probability A occurs
Probability B occurs
Probability that A & B occur

"The probability P(E) of an event E is a real number in the range of 0 to 1. The probability of an impossible event is 0 and that of an event certain to occur is 1."

The Law of Total Probability states that  P(A + B) is the probability that either A or B occur alone or that both occur together.

P(A + B) can be computed from: P(A + B) = P(A) + P(B) – P(A, B), where

  • P(A) = the probability that A occurs,
  • P(B) = the probability that B occurs, and
  • P(A, B) = the probability that both A and B occur simultaneously.

See Also