Warm - upLunch Choices

Power pointProbably Probability

Guided PracticeChance and Probability

Independent PracticeActivity: Is This Fair?

Probability and Statistics

Warm up

Lunch Choices

Tonya has lots of choices for lunch today. She gets to choose one food from each group:

1.How many different lunch combinations are possible?

2. What are the choices unique to peanut and jelly? Write as a fraction, decimal and percent.

Warm up

Lunch Choices

Main course2

x Fruit or vegetable2

Drink3

x = 12 outcomes

Main course Fruit or vegetableDrink

Pizza

Peanut butter & jelly

Low fat milk

Chocolate milk

Apple juice

Apple juice

Carrots & celery

Low fat milk

Chocolate milk

Apple juice

Apple juice

Carrots & celery

Low fat milk

Chocolate milk

Apple juice

Low fat milk

Chocolate milk

Apple juice

Warm up

Lunch Choices

2. What are the choices unique to peanut and jelly? Write the outcome as a fraction, decimal and percent.

Peanut butter & jelly/apple/low fat milk, Peanut butter & jelly/apple/chocolate milk, Peanut butter & jelly/apple/apple juice, Peanut butter & jelly/carrots & celery sticks/low fat milk, Peanut butter & jelly/carrots and celery sticks/chocolate milk, Peanut butter & jelly/carrots and celery sticks/apple juice

12

0.5 50%

Probably Probability

What is probability?

Probability is the mathematics of chance. It is the prediction of an outcome over a series of events ( things that happen/occur).

They use phrases such as not likely, no way, and probably as in everyday speech. Are these really probability terms?

We often hear and use statements of probability in our daily lives.

Listen to weather forecasts when they wonder whether a game will be held or that the chance that school is canceled.

We choose an event, then the probability of that event is found by counting the number of times the event is true (favorable) and dividing by the total number of possible and equally likely outcomes.

Probabilities are expressed as ratios, fractions, decimals, or percents.

They are determined by considering the results of an experiment.

Simple probability is when we conduct a one stage or one object experiment.

P(event) = number of true outcomes total number of equally likely outcomes

Probably Probability

Since it is equally likely get heads or tails, the probability (chance) of flipping a coin and having the outcome a tail is 50%.

A Simple Experiment

When you flip a coin, how many possible outcomes are there?

The experiment

The sample space

The coin could land showing a head or a tail. The list of all possible outcomes is called the sample space. The sample space in this experiment is heads or tails (H,T).

P(event) = number of true outcomes total number of equally likely outcomes

 1 2P (tail) =

Probably Probability

Chance

What are the possible outcomes?

2

A bag contains 6 blue marbles, 6 red marbles, 3 green marbles, and 5 yellow marble.

Probably Probability

1. What is the probability of drawing a red marble?

2. What are the chances of not drawing a red? Write the answer as a fraction, decimal, and a percent.

, This means there is a 70% chance of not drawing a red marble.

There are 20 marbles in the bag and 6 out of the 20 are red marbles.

P (red) = 310

620

or

14 out of the 20 marbles are not red. 710

1420

= or 0.7 of the marbles are not red.

P (not red) = 710

1420

or

710

, 0.7, 70%

The possibility that an event will happen ranges from impossible to certain on the probability line.

If something has the same chance of happening as it has of not happening, it is said to be an equally likely (50 %).

Probabilities are always written as fractions, decimals or percentages

Probably ProbabilityChance

Probably ProbabilityChance

Determine where each of the probabilities would appear on the probability line?

a. The probability of drawing a red marble from a bag of red marbles?

b. The probability of rolling a 5 on one roll of a die.

c. The probability of getting both heads or both tails when flipping a coin twice.

d. The probability of drawing a white marble from a bag of red marbles.

Certain,

16

23

16 % 0.16Unlikely,

Equally likely to happen or not happen,12 0.5

Impossible,

1 100%

50%

0%0

Probably Probability

Parker’s teacher uses a spinner to determine the order in which each group will make their math presentation. Use the spinner to find each probability in simplest terms.

a. P (group 6)

c. P (group 2 or 5)

b. P (not group 6)

d. P (not group 1, 3, or 4)

e. P (group numbered less than 5)

f. P (group 8)

16

5613

12

23

0 06

Discuss with a partner the answers and be prepared to share with the class.

Maybe-Maybe Not

1. The table shows the membership of the student council at Holmes Middle School.Suppose one student is to be selected randomly as the president. Find theprobability of each event in simplest form.

Guided Practice

Girls 30

Boys 20

8th graders 25

7th graders 15

6th graders 10

Student Council

P (5th grader)

P (girl)

P (boy)

P (6th or 8th grader)

P (not 7th grader)P (boy or girl)

35

25

710

7101

0

Maybe-Maybe Not

2. Randomly choose one of the tiles 1-9. Find the favorable outcomes of each event.

b. choosing 6 or 9

a. Choosing a number greater than 3 c. Choosing not an odd number

e. Choosing a odd number less than 5

d. Choosing a number divisible by 329

49

23

29

13

Guided Practice

Is This Fair?Independent Practice

• Can you decide if Game A or Game B is fair based on the probability of your game results?

• What is a fair game?

Is This Fair?Independent Practice

• Work in pairs or groups of four with two players on a team.

• Materials– Paper bag– 2 red and 3 blue cubes

• You will play two games– Game A uses 2 blue and 2 red cubes– Game B uses 3 blue cubes and 1 red cube

Is This Fair?Independent Practice

• Game Rules– One team is the red team and the other is the

blue team– Red and blue cubes are placed in a bag– Teams take turns reaching in without looking,

removing one cube, examining and recording its color, and replacing it.

– A game will consist of 20 draws– The winner is the team that has drawn the most

cubes matching the team color.

Is This Fair?Independent Practice

• Is Game A fair? Explain using probability.

• Is Game B fair? Explain using probability.