Exercise 6 Page 719

P(A)+P(B)=P(A or B) + P(A and B) Let's focus on what each of the regions in the diagram represents, starting with the region where A and B overlap. This is called the intersection. The outcomes that belong to that region satisfy both A and B. We can refer to this region as (A and B).

All the outcomes that satisfy the events A or B can be thought as (A or B). Here the word or implies that the two conditions are not necessarily satisfied at the same time.

Now, since events A and B overlap, when P(A) and P(B) are added, the probabilities of the the outcomes in the intersection are counted twice. In P(A or B), on the other hand, all the outcomes from the intersection are counted once, which is why the probabilities are not equal. P(A)+P(B)≠ P(A or B) Only by adding the probability of (A and B) to the left-hand side are the probabilities of the outcomes from the intersection counted twice on both sides. This gives us an equality. P(A)+P(B)=P(A or B) + P(A and B)