AP Statistics Section 6.3 A Probability Addition Rules

Recall these rules of probability:

Consider the table at the right about Nobel Prize winners. If one winner is selected at random, find…. P(from the U.S.) = P(in medicine) = P (from the U.S. or in medicine) =

If events A and B are not disjoint, then they have some outcomes in common.

NEW and IMPROVED ADDITION RULE: Note: If A and B are disjoint, then and the Addition Rule above is obtained.

We can use Venn diagrams to illustrate non-disjoint events.

Example 1: The probability that Deborah is promoted, P(D), is 0.7. The probability that Matthew is promoted, P(M), is 0.5. The probability that both Deborah and Matthew are promoted, P(D and M), is 0.3.

Find P(Deborah is promoted but Matthew is not)

Find P(that at least one of them is promoted)

Find P(neither one is promoted)

Example 2: Stephanie is graduating from college. Here are the probabilities for her obtaining three jobs.

A B C

(a) P(Stephanie is offered at least one of three jobs) (b) P(Stephanie is offered jobs A and B but not C)