This document discusses the addition rules for probability of compound events. It defines mutually exclusive events as events that cannot occur at the same time, and explains that for mutually exclusive events A and B, the probability of A or B is equal to the probability of A plus the probability of B. For events that are not mutually exclusive, the probability of A or B is equal to the probability of A plus the probability of B minus the probability of A and B occurring together. Several examples are provided to illustrate calculating probabilities using these addition rules.

1. 4-3 The Addition Rules For Probability

2. OBJECTIVE
 To find the probability of compound events,
using the addition rules.

3. MUTUALLY EXCLUSIVE EVENTS
 Two events are mutually exclusive if they
cannot occur at the same time (i.e., they
have no outcomes in common).

4. ADDITION RULE 1
 When two events A and B are mutually
exclusive, the probability that A or B will
occur is P(A or B) = P(A) + P(B)

5. ADDITION RULE 2
 If A and B are not mutually exclusive events,
then P(A or B) = P(A) + P(B) – P(A and B).

6. EXAMPLE
 Mutually exclusive or not?
 Getting a 7 and getting a jack
 Getting a club and getting a king
 Getting a face card and getting an ace
 Getting a face card and getting a spade

7. EXAMPLE
 A box contains 3 glazed doughnuts, 4 jelly
doughnuts, and 5 chocolate doughnuts. If a
person selects a doughnut at random, find
the probability that it is either a glazed
doughnut or a chocolate doughnut.
 8/12 or 2/3 or 66.7%

8. EXAMPLE
 At a political rally, there are 20 Republicans,
13 Democrats, and 6 Independents. If a
person is selected at random, find the
probability that he or she is either a
Democrat or an Independent.
 19/39 or 48.7%

9. EXAMPLE
 A day of the week is selected at random.
Find the probability that it is a weekend day.
 2/7 or 28.6%

10. EXAMPLE
 A single card is drawn from a deck. Find the
probability that it is a king or a club.
 16/52 or 4/13 or 30.8%

11. EXAMPLE
 In a hospital unit there are 8 nurses and 5
physicians; 7 nurses and 3 physicians are
females. If a staff person is selected, find the
probability that the subject is a nurse or a
male.
 10/13 or 76.9%

12. EXAMPLE
 On New Year’s Eve, the probability of a
person driving while intoxicated is 0.32, the
probability of a person having a driving
accident is 0.09, and the probability of a
person having a driving accident while
intoxicated is 0.06. What is the probability of
a person driving while intoxicated or having a
driving accident?
 35%

13. THREE EVENTS
 Mutually Exclusive:
P(A or B or C) = P(A) + P(B) + P(C)
 Not Mutually Exclusive:
P(A or B or C) = P(A) + P(B) + P(C) – P(A and B) –
P(B and C) – P(A and C) + P(A and B and C)

14. ASSIGNMENT
p.193-196, #1, 2, 3-25 odd