What are the chances……

Of winning a football game? Of getting Bingo? Of a coin landing on tails twice after being flipped twice? Of winning a race?

What are the chances of finding a magic lamp with a genie inside? Is there a chance of a snow day? PROBABILITY IS EVERYWHERE!!!!!! How about swimming with mermaids?

Define probability Determine if a game is “fair” Calculate theoretical and experimental probability Conduct an experiment Display the results Use a tree diagram to help solve probability problems Complete the PROBABILITY FINAL PROJECT

Probability Check List You are responsible for the following activities and they should be handed in all together.  Complete Fraction Review Page  Complete “Probability 1”  Complete Penny Game Table  Complete “Probability 2”  Complete Rock-Paper-Scissor  Complete Final Project

WHAT IS PROBABILITY? Probability is the likelihood that an event will occur. What is the probability of landing on red? What are the chances of landing on a shade of green?

In a perfect world, teams would all be equal in size, talent and ability. What things can impact the probability of winning a game?

What are the chances that the sun will set tonight? What are the chances that you will roll a 7 on a 6-sided die? What are the chances of it raining on Sunday? Chance is the possibility of an outcome in a certain event. An event is a happening or occurrence. An outcome is a result of an event.

The probability of the Chiefs winning the Super Bowl is.03…… OR IS IT????? MORE IMPORTANTLY: WHAT DOES THAT MEAN?????

What do the numbers mean?  If the probability is 0, the event is impossible.  The closer the probability is to 1, the more likely it will occur.  The closer the probability is to 0, the less likely it will occur.  If the probability is 1, the event is certain.

So what does that mean for the Kansas City Chiefs? With a probability of.03, it is not likely that they will win the Super Bowl this year. Keep in mind that this is assuming all teams have an equal chance of winning the Super Bowl, but do they????????

How can probabilities be written?  As a fraction: ¼  As a decimal:.25  As a percent: 25%

We better review! Use the links below to review fractions, decimals and percents. Change a fraction to a percent Change a decimal to a percent Simplify Fractions Change a fraction to a decimal Fraction Review Sheet Complete fraction review sheet

Fraction Review SheetName _________ Put the following fractions in simplest form: Change the following fractions to decimals: Change the following fractions and decimals to percents:

 Flipping a penny and it lands on tails?  Use the spinner and land on red?  Rolling a 6-sided die and getting a 5? ProbabilityNext Slide 1

PROBABILITY 1 Name_________ 1. You roll a 6-sided die. a. What is the probability that you will roll a 4? P (4) = b. What is the probability that you will roll a 2 or 5? P (2 or 5) = c. What is the probability that you will roll an even number? P (Even) = You spin the spinner at the right. d. What is the probability of landing on green? P (green) = a. What is the probability of not landing on yellow? P (not yellow) = b. What is the probability of landing on blue or red? P (blue or red) = 2. You have a standard deck of 52 playing cards. a. What is the probability of picking a nine? P (9) = b. What is the probability of picking a diamond? P (diamond) = c. What is the probability of picking a black card? P (black card) = d. What is the probability of picking a face card? P (face card) =

How can we calculate probabilities? There are four common ways to calculate probabilities:  Make a guess  Conduct an experiment  Use a data table  Assume that all possible results have the same chance

Penny Game Directions:  Get a partner, a penny, and a game sheet  You are going to flip the penny two times.  If the coin lands tails up both times player A gets 1 point. Any other outcome, Player B gets 1 point. GameNext Slide sheet

Penny Game Sheet During each round, you will need to flip the penny two times. Player A: Player B: Penny Tracking Rounds: Flip #1 Flip #

Do you think this game is fair? A fair game is a game in which each player or team has the same chance of winning. If any player or team has an advantage or disadvantage, then the game is not fair.

Rock Paper Scissors

HOW MANY POSSIBLE OUTCOMES ARE THERE? We should display all the possibilities, BUT HOW DO WE DO THAT???

Using a Table: Player 1Player 2 Rock PaperRock ScissorRock Paper ScissorPaper RockScissor PaperScissor

USE A LIST Rock-RockPaper-RockScissor-Rock Rock-PaperPaper-PaperScissor-Paper Rock-ScissorPaper-ScissorScissor-Scissor

USE A TREE DIAGRAM Rock PaperScissor RockRock RockRock RockRock PaperPaper PaperPaper PaperPaper ScissorsScissors ScissorsScissors ScissorsScissors

What is the probability that you will win at Rock Paper Scissor? Let’s look at the possible outcomes from our tree diagram Scissor-Scissor Scissor-Paper Scissor-Rock Paper-Scissor Rock-Rock Paper-Paper Paper-Rock Rock-Scissor Rock-Paper You could win 3 different ways

How many possible outcomes did we find in our tree diagram??? tree How many times could we win? Now we turn what we know into a fraction: P (winning) = Number of times we could win Total possible outcomes

P(winning)= 3939 The chances of events happening as determined by calculating results that would occur under ideal circumstances. Is that in simplest form??? 1313 = Theoretical Probability

QUESTION: If you flip a coin twice how many possible outcomes are there? (Use a tree diagram to show these outcomes) When you are ready complete “Probability 2” Probability

POBABILITY 2 Name ___________ 1. You flip a coin three times. Use a table, list or tree diagram to display the total number of outcomes. 2. You roll a 6-sided die twice. Use a table, list or tree diagram to display the total number of outcomes.

Experimental Probability: The chances of something happening, based on repeated testing and observing results. It is the ratio of the number of times an event occurred to the number of times tested.

You will be playing with a partner and recording the results on the Rock, Paper, Scissor Data Table. Rock-Paper-Scissor Data Table

Let’s Compare Our theoretical probability was 1/3. What was your experimental probability?

Let’s Look at An Example Miss M and Mrs. D’s Game Table Based on their results what is the probability of Miss M winning? 2 out of 10 Based on their results what is the probability of Mrs. D winning? 4 out of 10 Based on their results what is the probability of it being a tie? 4 out of 10

Can we graph our results?

How About a Bar Graph???

Let’s Think What things might influence our experimental probability?

LET’S WRAP UP! What is probability? How can we represent the possible outcomes? Are all games fair? What is difference between theoretical and experimental probability? Is Probability Fun?

1.Design a two-player game- It may use coins, dice, spinners, etc. 2.Collect data (table) 3.Display data (Graph) 4.Conduct analysis of game ( tree diagram) 5.Explain why your game is or is not fair 6.Include a peer-review from a classmate FINAL PROJECT

Probability Check List These are the assignments that need to be handed in. Use the buttons on the right to take you back to the corresponding pages.  Complete Fraction Review Page  Complete “Probability 1”  Complete Penny Game Table  Complete “Probability 2”  Complete Rock-Paper-Scissor  Complete Final Project F P1 G P2 R P

Adapted from cts/Projects/Probability/PROBABILITY Clip Art - Peanut Comic Strips - Bingo pic, penny guy, runner, penny flip dice rain, balance genie, flounder

Sound files Peanuts theme song- jeopardy- Monday night football Text Everyday Learning Corporation. Everyday Mathematics: Student Reference Book. Everyday Learning. Chicago, Illinois,1998.

Photos sunsethttp://dgl.microsoft.com/?CAG=1

Fraction Review SheetName _________ Put the following fractions in simplest form: Change the following fractions to decimals: Change the following fractions and decimals to percents:

Penny Game Sheet During each round, you will need to flip the penny two times. Player A: Player B: Penny Tracking Rounds: Flip #1 Flip #

POBABILITY 2 Name ___________ 1. You flip a coin three times. Use a table, list or tree diagram to display the total number of outcomes. 2. You roll a 6-sided die twice. Use a table, list or tree diagram to display the total number of outcomes.

Rock-Paper-Scissor During each round you need to record each players signal and who won that round. Use “T” if there is a tie. Rules: Rocks beat scissor Paper beats rock Scissor beats paper Game Tracking Game TrackingRounds: Player A Player B Who won: ExampleScissorRockB

Rock-Paper-Scissor During each round you need to record each players signal and who won that round. Use “T” if there is a tie. Rules: Rocks beat scissor Paper beats rock Scissor beats paper Game Tracking Game TrackingRounds: Player A: Miss M Player B: Mrs. D Who won: ExampleScissorRockB 1RP Mrs. D 2SR 3RRT 4PPT 5PS Miss M 6RP Mrs. D 7RP 8SST 9PR Miss M 10PPT