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: Find each Probability
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.

8. Section 3.4
Additional Topics in Probability & Counting

9. 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

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

11. EXAMPLES
20. 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?

12. 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!)

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

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

15. 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?