The Probability of Either of Two Events or Both Occurring



If P(A) and P(B) are the probabilities that events A and B will occur, the probability P(A + B) that either A or B or both will occur is:

Example:
Let's say one wants to determine the probability of choosing an Ace or a Ten from a randomly shuffled deck of cards. We know that there are 4 four Aces in the deck. We know there are 16 Ten valued cards in the deck. We also know that there are 52 cards in the deck. Therefore, we can say that the probability P(A) of selecting one of the four Aces from the 52 card deck is P(A) = m/n = 4/52 = 0.07692307692308. We can also say that the probability of selecting a Ten valued card P(B) = m/n = 16/52 = 0.3076923076923 The probability that both an Ace and a Ten can be selected at the same time P(A,B) = 0. Therefore, the probability of choosing either an Ace or a Ten from a randomly shuffled deck of cards is P(A+B) = P(A) + P(B) - P(A,B) = 0.07692307692308 + 0.3076923076923 - 0 = 0.384615384615


NOTE:
The + sign in the P(A+B) term does not mean "plus". Instead, it means "or". So, P(A+B) is read as follows: "The probability of A or the probability of B".