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

The Addition Rule

Mutually Exclusive EventsTwo events A and B are mutually

exclusive if A and B cannot occur at the same time.

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

The Addition RuleThe 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)

EX: From p 16214.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.

a) Rolling a 5 or a number greater than 3.

b)Rolling a number less than 4 or an even number.

c) Rolling a 2 or an odd number.

18. You roll a die. Find each Probability

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

TOTAL 428 886 1536 2850

#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.

Additional Topics in Probability & Counting

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

Permutations of n objects taken r at a time…Notation: nPr

nPr = n!

(n – r)!

ORDER MATTERS!!!

EXAMPLESEight 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?

Distinguishable PermutationsThe 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!)

EXHow many distinguishable

permutations are there using the letters in the word ALPHA?

In the word COMMITTEE?

CombinationsA selection of r objects from a group of

n objects is denoted nCr

nCr = n!

(n – r)!r!

ORDER DOES NOT MATTER!!!

EXA 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?