10.1 & 10.2

Probability & Permutations

WARM UP:

Term Definition ExampleTrial

Experiment

Sample SpaceEvent

A systematic opportunity for an event to occur

One or more trials

rolling a die

rolling a die ten times

The set of all possible outcomes 1, 2, 3, 4, 5, 6

An individual outcomeor

Any specified combination of outcomes

rolling a 3

rolling a 3 or rolling a 5

Outcomes are random if all

Probability is expressed as a number between 0 and 1. It can be written as a

An impossible event

An event that must occur has a

The sum of the probabilities of all outcomes in the sample space is

fraction, decimal, or percent.

possible outcomes are equally likely.

has a probability of 0.

probability of 1.

1.

Approximated by performing trials and recording the ratio of

Experimental Probability:

the number of occurrences of the event to the number of trials.

1a. Find the probability of randomly selecting a blue marble in one draw from a bag containing 2 red marbles, 4 blue marbles, and 3 yellow marbles.

The event is one blue marble.

Because there are 4 blue marbles, the number of outcomes in the event is 4.

The sample space is the set of all marbles, so the total number of outcomes in the sample space is 2 + 4 + 3, or 9.

number of outcomes in the event(1 blue marble)

number of outcomes in the sample space

4, or about 44%

9

P

The Fundamental Counting Principle

If there are m ways that one event can occur and n ways that another event can occur, then

there are m x n ways that both events can occur.

Probability versus Odds

If one day of the week is randomly chosen, the probability that the chosen day will be Tuesday is:

1, or about 14%

7

If one day of the week is randomly chosen, the odds that Wednesday will be chosen are: 1 to 6

Odds, expressed a ratio, compare the chance of an event happening to the chance of it NOT happening.

Ex 6. There are 1200 students at South Penn High School, 760 of whom are boys.What are the odds of a girl being randomly chosen to win concert tickets?

There are 1200-760, or 440 girls, so the odds of a girl being chosen can be found by comparing the chances of a girl being chosen to the chances that a girl is NOT chosen.

440 to 760

Or 11 to 19

10.2 - Permutations