1. Addition Rules of Probability……

2. OBJECTIVE Recognize Mutually Exclusive Events
Use the Addition Rule of Probability

3. RELEVANCE
To find the likelihood of an event occurring by observing the long-term proportion in which a certain outcome is observed.

4. Card Facts…… 52 cards in the deck 4 suits
13 cards in each suit (diamond, hearts, clubs, spades)
Face cards – jack, queen, king
26 red cards; 26 black cards

5. Mutually Exclusive Events……
Events that cannot occur at the same time.
For example:
Being a junior and being a senior are mutually exclusive.

6. Determine which events are mutually exclusive when a single die is rolled…..
Getting a 4 and a 6
Getting an odd # and an even #
Getting an odd# and a # less than 4
Getting a # greater than 4 and a # less than 4
Getting a 3 and an odd #
Mutually Exclusive
Not M.E.

7. You Try…Which are mutually exclusive when a single card is drawn from a deck?......
Getting a 7 and J
Getting a club and king
Getting a face card and an ace
Getting a face card and a spade
M.E
Not M.E.
M.E.

8. Addition Rule – M.E. Events……
When 2 events are mutually exclusive, the probability that A or B will occur is

9. Example……
A box contains 3 glazed, 4 jelly, and 5 chocolate doughnuts. If a person selects one doughnut at random, find the probability that it is either glazed or chocolate.

10. Answer…… Sample Space = 3+4+5 = 12 doughnuts
P(glazed or choc) = P(glazed) + P(chocolate)

11. 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.

12. Answer……
Sample Space = =39
P(dem or ind) = P(dem)+P(ind)

13. Example……
A day of the week is selected at random. Find the probability that it is a day of the weekend.

14. Answer…… Sample Space = 7 days in a week
P(Sat or Sun)= P(Sat) + P(Sun)

15. Addition Rule – NOT Mutually Exclusive……
When 2 events are NOT mutually exclusive, the probability that A or B will occur is
The Formal Addition Rule

16. Example……
A single card is drawn from a deck. Find the probability that it is a king or club.

17. Example……
In a hospital unit there are 8 nurses and 5 doctors. 7 nurses and 3 doctors are female. If a staff person is selected, find the probability that the subject is a nurse or a male.
Suggestion: Make a contingency table.

18. Find the P(nurse or male)
Females
Males
Total
Nurse 7 1 8
Doctors 3 2 5 10 13
Let n = nurse and m = male
P(n or m) =
P(nurse) + P(m) – P(nurse and male)

19. Example……
On New Year’s Eve, the probability of a person driving while intoxicated is 0.32, the prob. of a person having an accident is .09, and the prob. of a person having an accident while intoxicated is What is the probability of a person driving while intoxicated or having an accident?

20. Answer……
P(intox or acc) =
P(intox) + P(acc) – P(intox and acc)