Probability

What are the chances of that happening?

Vocab:

ProbabilityChance an outcome will occur

RandomOccurs by chance

Calculating Probability

P(event)= number of favorable outcomes number of possible outcomes

Can be written as a• Fraction• Decimal• Percent

Simple Probability

A fair dice is thrown once. Find the probabilities that the score is:

(a) Bigger than 3,

(b) An odd number,

(c) Bigger than 3 and a prime number,

(d) Bigger than 3 or a prime number, but not both.

Simple Probability

A card is chosen at random from an ordinary pack. Find the probability that it is:

(a) Red,

(b) A face card (Ace, King, Queen or Jack),

(c) Red, or a picture card, or both,

Cards

A

K

Q

J

10

9

8

7

6

5

4

3

2

A

K

Q

J

10

9

8

7

6

5

4

3

2

A

K

Q

J

10

9

8

7

6

5

4

3

2

A

K

Q

J

10

9

8

7

6

5

4

3

2

ASSIGNMENT

WB 9-1

Tree Diagrams

Use for compound events Find all possiblities

Problem 1

Joe has a blue pair of pants and a black pair of pants. He had a white shirt, a yellow shirt, and a blue shirt. How many possible outfit choices does he have?

Another way to solve the problem…. Fundamental Counting Principle

Simple mutliply the number of options for each event.

2 pants & 3 shirts2 x 3 = 6

Problem 2

The Greasy Spoon Restaurant offers 6 appetizers and 14 main courses. In how many ways can a person order a two-course meal?

Solution:6 ∙14 = 84

College Classes

Next semester, a college student is planning to take three courses – math, English and science. There are 8 sections of math,5 of English, and 4 of science that she finds suitable.How many different three-course schedules are possible?

Solution:This situation involves making choices with three groups of items.

Math English Humanities {8 choices} {5 choices} {4 choices}

There are 8∙5∙4 = 160 different three-course schedules.

Telephone Numbers in the USA

Telephone numbers in the United States begin with three-digit area codes followed by seven-digit local telephone numbers. Area codes and local telephone numbers cannot begin with 0 or 1. How many different telephone numbers are possible? Solution: This situation involves making choices with ten groups of items. Here are the choices for each of the ten groups of items: Area Code Local Telephone Number 8 10 10 8 10 10 10 10 10 10

The total number of different telephone numbers is: 8 ∙ 10 ∙ 10 ∙ 8 ∙ 10 ∙ 10 ∙ 10 ∙ 10 ∙ 10 ∙ 10 = 6,400,000,000

Permutations

Permutation is an ordered arrangement of items that occurs when:

No item is used more than once.

The order of arrangement makes a difference.– Gold, Silver, Bronze Metals

Example 1Counting Permutations

You are in charge of planning a concert tour with U2, ‘N Sync, Aerosmith and the Rolling Stones. You decide that the Rolling Stones will perform last. How many different ways can you put together the concert?

Solution: You can now choose any one of the three groups, U2, ‘N sync or Aerosmith, as the opening act. That leaves two groups left to choose from for the second group and only one group left for the third group.

Using the Fundamental Counting Principle there are: 3∙2∙1∙1 = 6 different ways to arrange the concert.

Math--

In how many distinct ways can the letters of the word MATH be arranged?

Solution:The word contains 4 letters. After a letter is used, it can not be used again. The number of distinct permutations are:

4 x 3 x 2 x 1 = 24

Combination

Combination is an ordered arrangement of items that occurs when:

No item is used more than once.

The order of arrangement does NOT makes a difference.– Tennis Doubles