14.7 Probability and Odds

CORD MathMrs. Spitz

Spring 2007

Lesson Objectives

• Find the probability of an event.• Find the odds of an event.

Assignment:Worksheets 2.8 A, B and C by Friday. Turn in one today!

Probability of an event

• The probability of an event is a measure of the likelihood that the event will occur. It is a number between 0 and 1, inclusive

P = 0

Impossible

P = 0.25

Unlikely

P = 0.5

Happens half the time

P = 0.75

Very likely

P = 1

Absolutely will happen

Outcomes

• When you do a probability experiment, the different possible results are called the outcomes. When an experiment has N equally likely outcomes, each of them occurs with probability 1/N. For example, in the roll of a six-sided number cube (i.e. dice—don’t you just love math?), the possible outcomes are 1, 2, 3, 4, 5, and 6 and the probability associated with each outcome is 1/6.

Favorable outcomes

• An event consists of a collection of outcomes. In the roll of a six-sided number cube, an “even roll” consists of the outcomes 2, 4, and 6. The theoretical probability of an even roll is 3/6 or ½. The outcomes for an event you wish to have happen are called favorable outcomes, and the theoretical probability of this event is calculated by the following rule:

P = # of favorable outcomes Total # of outcomes

Ex. 1: Finding the probability of an event

You toss two coins. What is the probability that both are heads?

ANSWER:There are four possible outcomes that

are equally likely. (H,H), (H,T), (T,H), (T, T)

P = # of favorable outcomes = 1 = 0.25 Total # of outcomes 4

Ex. 2: Probability of an event

• A CORD Math class has 17 boys and 16 girls. One student is chosen at random from the class. What is the probability P tht the student is a girl?

Ex. 2: Finding the probability of an event

Because the student is chosen at random, it is equally likely that any of the 33 students will be chosen. Let “number of girls” be the favorable outcome. Let “number of students” be the total number of outcomes.

ANSWER:P = # of favorable outcomes = 16 =

0.485 Total # of outcomes 33

Experimental Probability

• Another type of probability is experimental probability. This type of probability is based on repetitions of an actual experiment and is calculated by the following rule:

P = Number of favorable outcomes Total # of trials

Surveys

A survey is a type of experiment. Probability based on the outcomes of a survey can be used to make predictions.

Ex. 3: Using a survey to find a probability

• Use the circle graph at the right showing the responses of 500 teens to a survey asking “Where would you like to live?”

• If you were to ask a randomly chosen teen this question, what is the experimental probability that the teen would say “large city?”

Where would you like to live?

Large City(155)

Small town(90)Suburbs(100)

Rural/Ranch(70)

Wilderness(85)

Large City(155)

Small town(90)

Suburbs(100)

Rural/Ranch(70)

Wilderness(85)

Solution

• Let “number choosing large city” be the favorable outcome. Let “number surveyed” be the total number of outcomes.

P = Number choosing large city 155 Number surveyed 500

P = 0.31

=

Finding the Odds of an event

• When all outcomes are equally likely, the ODDS that an event will occur is given by the formula below:

Odds = Number of favorable outcomes Number of of unfavorable

outcomes

Ex. 4: Finding the odds of an event

• You randomly choose an integer from 0 through 9. What are the odds that the integer is 4 or more?

Ex. 4: Finding the odds of an event

SOLUTION:There are 6 favorable outcomes, 4, 5, 6,

7, 8, and 9. There are four unfavorable outcomes 0, 1, 2, 3.

Odds = Number of favorable outcomes Number of unfavorable outcomes

2

3

4

6 The odds that the integer is

4 or more are 3 to 2.

ODDS

If you know the probability that an event will occur, you can find the odds.

Odds = Probability event will occur Probability the event will not

occurIs equal to: Probability event will occur 1 – (Probability event will occur)

Ex. 5: Finding Odds from probability

• The probability that a randomly chosen household has a cat is 0.27. What are the odds that a household has a cat?

Odds = Probability the event will occur 1 – (Probability the event will occur)

73

2773.0

27.027.01

27.0

Substitute for probabilities

Simplify the denominator

Multiply numerator and denominator by 100 to get rid of decimals.

The odds are 27 to 73 that a randomly chosen household has a cat.