A First Course in Statistics, 12th Edition

3.4 The Additive Rule and Mutually Exclusive Events

In Section 3.2, we saw how to determine which sample points are contained in a union of two sets and how to calculate the probability of the union by summing the separate probabilities of the sample points in the union. It is also possible to obtain the probability of the union of two events by using the additive rule of probability.

By studying the Venn diagram in Figure 3.11, you can see that the probability of the union of two events A and B can be obtained by summing P(A) and P(B) and subtracting $P(A\cap B)$. We must subtract $P(A\cap B)$ because the sample point probabilities in $A\cap B$ have been included twice—once in P(A) and once in P(B).

Figure 3.11

Venn diagram of union

The formula for calculating ...