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What are the chances……

Learn about probability and its applications in football games, bingo, coin flips, and other scenarios. Understand theoretical and experimental probability, conduct experiments, and solve probability problems using tree diagrams. Complete activities and a final project to enhance your understanding.

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What are the chances……

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  1. What are the chances……

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

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

  4. Where do you see probability?

  5. At the end of this unit you will be able to do the following: • 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

  6. 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

  7. 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?

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

  9. 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 eventis a happening or occurrence. An outcome is a result of an event.

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

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

  12. 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????????

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

  14. OH NO FRACTIONS!

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

  16. Fraction Review SheetName _________ Put the following fractions in simplest form: 1. 12 2. 15 3. 10 4. 8 18 24 25 18 Change the following fractions to decimals: 5. 1 6. 3 7. 8 8. 6 4 5 9 10 Change the following fractions and decimals to percents: 9. 3 10. 1 11. .54 12. .257 4 2

  17. What's the probability of: • Flipping a penny and it lands on tails? • Rolling a 6-sided die and getting a 5? • Use the spinner and land on red? ProbabilityNext Slide 1

  18. 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) =

  19. 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

  20. Let's Flip A Coin!

  21. 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

  22. Penny Game Sheet During each round, you will need to flip the penny two times. Player A: Player B: Rounds: Flip #1 Flip #2 1 2 3 4 5 6 7 8 9 10 Penny Tracking

  23. 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.

  24. Let's Try a Game Paper Scissors Rock

  25. HOW MANY POSSIBLE OUTCOMES ARE THERE? We should display all the possibilities, BUT HOW DO WE DO THAT??? Tree Diagram Table List

  26. Using a Table:

  27. USE A LIST Rock-Rock Paper-Rock Scissor-Rock Rock-Paper Paper-Paper Scissor-Paper Rock-Scissor Paper-Scissor Scissor-Scissor

  28. USE A TREE DIAGRAM Rock Paper Scissor Scissors Scissors Scissors Rock Rock Rock Paper Paper Paper

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

  30. 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

  31. Theoretical Probability The chances of events happening as determined by calculating results that would occur under ideal circumstances. 3 9 1 3 P(winning)= = Is that in simplest form???

  32. Your turn: 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

  33. 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.

  34. 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.

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

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

  37. 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

  38. Can we graph our results? OF COURSE WE CAN

  39. How About a Bar Graph???

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

  41. 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?

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

  43. 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

  44. Works Sited Adapted from http://www.nynetresources.org/Future%20Grant%20Projects/Projects/Probability/PROBABILITY Clip Art http://www.csun.edu/~hcmth014/comics.html - Peanut Comic Strips http://clipartuniverse.com/free-animation.shtml - Bingo pic, penny guy, runner, penny flip http://www.animationcity.net/animcity.htmdice http://dgl.microsoft.com/?CAG=1rain, balance http://disneyclipart.comgenie, flounder

  45. Works Sited Sound files http://soundamerica.com Peanuts theme song- jeopardy- Monday night football Text Everyday Learning Corporation. Everyday Mathematics: Student Reference Book. Everyday Learning. Chicago, Illinois,1998.

  46. Works Sited Photos http://dgl.microsoft.com/?CAG=1 sunset

  47. Fraction Review SheetName _________ Put the following fractions in simplest form: 1. 12 2. 15 3. 10 4. 8 18 24 25 18 Change the following fractions to decimals: 5. 1 6. 3 7. 8 8. 6 4 5 9 10 Change the following fractions and decimals to percents: 9. 3 10. 1 11. .54 12. .257 4 2

  48. Penny Game Sheet During each round, you will need to flip the penny two times. Player A: Player B: Rounds: Flip #1 Flip #2 1 2 3 4 5 6 7 8 9 10 Penny Tracking

  49. 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.

  50. 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 Rounds: Player A Player B Who won: Example Scissor Rock B 1 2 3 4 5 6 7 8 9 10

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