Transcript Presentation

Probability and Statistics
Warm - up
Lunch Choices
Power point
Probably Probability
Guided Practice
Chance and Probability
Independent Practice
Activity: Is This Fair?
Lunch Choices
Warm up
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.
Lunch Choices
Warm up
Main course
2
Main course
x Fruit or vegetable
2
Fruit or vegetable
x Drink = 12 outcomes
3
Drink
Low fat milk
Apple juice
Chocolate milk
Apple juice
Pizza
Low fat milk
Carrots & celery
Chocolate milk
Apple juice
Low fat milk
Apple juice
Peanut butter &
jelly
Chocolate milk
Apple juice
Low fat milk
Carrots & celery
Chocolate milk
Apple juice
Lunch Choices
Warm up
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
1
2
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).
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.
They use phrases such as not likely, no way, and probably as in everyday
speech. Are these really probability terms?
Probably Probability
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.
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.
P(event) =
number of true outcomes
total number of equally likely outcomes
Probably Probability
A Simple Experiment
The experiment
When you flip a coin, how many possible outcomes are there?
2
The sample space
What are the possible outcomes?
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
P (tail) =
1
2
Chance
Since it is equally likely get heads or tails, the probability (chance) of flipping a
coin and having the outcome a tail is 50%.
Probably Probability
A bag contains 6 blue marbles, 6 red marbles, 3 green marbles,
and 5 yellow marble.
1. What is the probability of drawing a red marble?
There are 20 marbles in the bag and 6 out of the 20 are red marbles.
P (red) = 6 or 3
10
20
2. What are the chances of not drawing a red? Write the answer as a fraction,
decimal, and a percent.
7 , 0.7, 70%
10
14
= 7 or 0.7 of the marbles are not red.
14 out of the 20 marbles are not red.
20
10
, This means there is a 70% chance of not drawing a red marble.
P (not red) = 14 or 7
20
10
Probably Probability
Chance
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 Probability
Chance
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?
Certain,
1
100%
b. The probability of rolling a 5 on one roll of a die.
1
2
Unlikely,
%
16
0.16
6
3
c. The probability of getting both heads or both tails when flipping a coin twice.
1
Equally likely to happen or not happen,
50%
0.5
2
d. The probability of drawing a white marble from a bag of red marbles.
Impossible,
0
0%
Probably Probability
Discuss with a partner the answers and be prepared to share with the class.
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.
1
a. P (group 6)
6
b. P (not group 6)
c. P (group 2 or 5)
5
6
1
3
1
d. P (not group 1, 3, or 4)
2
e. P (group numbered less than 5) 2
f. P (group 8)
0
0
6
3
Maybe-Maybe Not
Guided Practice
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 the
probability of each event in simplest form.
P (girl)
P (boy)
3
5
2
5
P
(6th
P
or
(5th
8th
7
grader)
10
grader)
0
P (not 7th grader)
P (boy or girl) 1
7
10
Student Council
Girls
30
Boys
20
8th graders
25
7th graders
15
6th graders
10
Maybe-Maybe Not
Guided Practice
2. Randomly choose one of the tiles 1-9. Find the favorable outcomes of each event.
2
a. Choosing a number greater than 3
3
b. choosing 6 or 9
2
9
c. Choosing not an odd number
4
9
d. Choosing a number divisible by 3
1
3
e. Choosing a odd number less than 5
2
9
Is This Fair?
Independent Practice
• What is a fair game?
• Can you decide if Game A or Game B is fair based on
the probability of your game results?
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.