1. Section 3.3
The Addition Rule

2. Mutually Exclusive Events
Two events A and B are mutually exclusive if A and B cannot occur at the same time.

3. EX: Decide if the events are mutually exclusive:
EVENT A
EVENT B
Randomly selecting a 20 year old student
Randomly selecting a student with blue eyes
Randomly selecting a vehicle that is a Ford
Randomly selecting a vehicle that is a Toyota
Randomly selecting a JACK from a deck of cards
Randomly selecting a FACE card from a deck of cards

4. The Addition Rule
The Probability that Event A OR Event B will occur is:
P(A or B) = P(A) + P(B) – P(A and B)
If A and B are mutually exclusive, then:
P(A or B) = P(A) + P(B)

5. EX: From p 162
A math conference has an attendance of 4950 people. Of these, 2110 are college profs and 2575 are female. Of the college profs, 960 are female.
a) Are the events “selecting a female” and “selecting a college prof” mutually exclusive?
b) The conference selects people at random to win prizes. Find the probability that a selected person is a female or a college prof.

6. 18. You roll a die. Find each Probability
Rolling a 5 or a number greater than 3.
Rolling a number less than 4 or an even number.
Rolling a 2 or an odd number.

7. 25. The table shows the results of a survey that asked 2850 people whether they were involved in any type of charity work. A person is selected at random.
Frequently
Sometimes
Not at all
TOTAL
Male
221
456
795
1472
Female
207
430
741
1378
428
886
1536
2850

8. #25 Continued…
A. The person is frequently or sometimes involved in charity work.
B. The person is female or not involved in charity work at all.
C. The person is male or frequently involved in charity work.
D. The person is female or not frequently involved in charity work.

9. Section 3.4
Additional Topics in Probability & Counting

10. Permutation:
… an ordered arrangement of objects. The number of different permutations of n distinct objects is n! n! = n(n – 1)(n – 2)(n – 3)….(3)(2)(1) NOTE: 0! = 1

11. Permutations of n objects taken r at a time…
Notation: nPr
nPr = n!
(n – r)!
ORDER MATTERS!!!

12. EXAMPLES
Eight people compete in a downhill ski race. Assuming that there are no ties, in how many different orders can the skiers finish?
A psychologist shows a list of eight activities to her subject. How many ways can the subject pick a first, second, and third activity?

13. Distinguishable Permutations
The number of distinguishable permutations of n objects, where n1 are of 1 type, n2 are of another type, and so on… is: n!
(n1!) (n2!) (n3!) .. (nk!)

14. EX
How many distinguishable permutations are there using the letters in the word ALPHA?
In the word COMMITTEE?

15. Combinations
A selection of r objects from a group of n objects is denoted nCr
nCr = n!
(n – r)!r!
ORDER DOES NOT MATTER!!!

16. EX
A three person committee is to be appointed from a group of 15 employees. In how many ways can this committee be formed?
If 6 of the 15 employees are women, what is the probability that a randomly chosen 3-person committee is all women?