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Introduction to Probability - Understanding Likelihood of Events

This lesson introduces students to the concept of probability and how to determine the likelihood of events. Students will learn about different probability terms, such as certain, impossible, likely, and unlikely, and how to calculate probabilities using fractions, decimals, and percents. They will also practice solving probability word problems and explore tree diagrams and area models to represent possible outcomes.

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Introduction to Probability - Understanding Likelihood of Events

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  1. 4/2/2015 March 12, 2015 • S-Sit and organize materials for the lesson… Get your journal and a sharpened pencil. • E-Examine and follow teacher’s directions…On your next blank page, write today’s date at the top. Title this page ~ Probability • T-Take the challenge! Write the CQ in journal below the title: Challenge Question: What operation do you use to solve compound probability if you see the word “and” in the word problem? What about if you see the word “or”? • Warm-Up: • What do you remember about probability from 5th and 6th grade? Make a list of everything you remember in your journal now!

  2. Review of Probability

  3. Presentation Probability • Probability is a measure of how likely an event is to occur. • For example – • Today there is a 60% chance of rain. • The odds of winning the lottery are a million to one. • What are some examples you can think of?

  4. Presentation Probability • Probabilities are written as: • Fractions from 0 to 1 • Decimals from 0 to 1 • Percents from 0% to 100%

  5. Presentation Probability • If an event is certain to happen, then the probability of the event is 1 or 100%. • If an event will NEVER happen, then the probability of the event is 0 or 0%. • If an event is just as likely to happen as to not happen, then the probability of the event is ½, 0.5 or 50%.

  6. Presentation Probability Impossible Unlikely Equal Chances Likely Certain 0 0.5 1 0% 50% 100% ½

  7. Presentation Probability • When a meteorologist states that the chance of rain is 50%, the meteorologist is saying that it is equally likely to rain or not to rain. • If the chance of rain rises to 80%, it is more likely to rain. • If the chance drops to 20%, then it may rain, but it probably will not rain.

  8. Presentation Probability • What are some events that will never happen and have a probability of 0%? • What are some events that are certain to happen and have a probability of 100%? • What are some events that have equal chances of happening and have a probability of 50%?

  9. Presentation Probability • The probability of an event is written: P(event) = number of ways event can occur total number of outcomes

  10. Presentation Probability P(event) = number of ways event can occur total number of outcomes • An outcome is a possible result of a probability experiment • When rolling a number cube, the possible outcomes are 1, 2, 3, 4, 5, and 6

  11. Presentation Probability P(event) = number of ways event can occur total number of outcomes • An event is a specific result of a probability experiment • When rolling a number cube, the event of rolling an even number is 3 (you could roll a 2, 4 or 6).

  12. Presentation Probability P(event) = number of ways event can occur total number of outcomes What is the probability of getting heads when flipping a coin? P(heads) = number of ways = 1 head on a coin = 1 total outcomes = 2 sides to a coin = 2 P(heads)= ½ = 0.5 = 50%

  13. Learning together Try These: 1. What is the probability that the spinner will stop on part A? B A C D • What is the probability that the spinner will stop on • An even number? • An odd number? 3 1 2 3. What is the probability that the spinner will stop in the area marked A? A C B

  14. Learning together Probability Word Problem: • Lawrence is the captain of his track team. The team is deciding on a color and all eight members wrote their choice down on equal size cards. If Lawrence picks one card at random, what is the probability that he will pick blue? Number of blues = 3 Total cards = 8 3/8 or 0.375 or 37.5% blue blue green black yellow blue black red

  15. Learning together Let’s Work These Together • Donald is rolling a number cube labeled 1 to 6. What is the probability of the following? a.) an odd number odd numbers – 1, 3, 5 total numbers – 1, 2, 3, 4, 5, 6 b.) a number greater than 5 numbers greater – 6 total numbers – 1, 2, 3, 4, 5, 6 3/6 = ½ = 0.5 = 50% 1/6 = 0.166 = 16.6%

  16. Learning together Try These: 1. What is the probability of spinning a number greater than 1? 1 2 3 4 • What is the probability that a spinner with five congruent sections numbered 1-5 will stop on an even number? 3. What is the probability of rolling a multiple of 2 with one toss of a number cube?

  17. Review of Total possible outcomes

  18. Presentation Tree Diagram – Total Possible Outcomes • Make a tree diagram to represent the following situation: I have 3 different colored marbles in a bucket (red, yellow, and blue) and a number cube (dice). If I draw out one marble from the bucket and roll the dice once, what are all the possible outcomes? 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 Red How many total possible outcomes? Blue Yellow

  19. Presentation Area Model – Total Possible Outcomes • Make an area model to represent the following situation: I have 3 different colored marbles in a bucket (red, yellow, and blue) and a number cube (dice). If I draw out one marble from the bucket and roll the dice once, what are all the possible outcomes?

  20. Review of How to calculate Probability of compound events

  21. Presentation “And” vs. “Or” • I have 3 different colored marbles in a bucket (red, yellow, and blue) and a number cube (dice). If I draw out one marble from the bucket and roll the dice once: • What is the probability of drawing a yellow and rolling an even? • What is the probability of drawing a yellow or rolling an even?

  22. Presentation “With replacement” vs. “Without replacement” • With replacement ~ the object is replaced before the next object is drawn (the total stays the same for both probabilities) • Ex. You have a bucket with 10 marbles (5 blue, 3 red and 2 green). What is the probability of drawing a blue, replacing it, and then drawing a green? • Without replacement ~ the object is not replaced before the next object is drawn (the total is different for both probabilities) • Ex. You have a bucket with 10 marbles (5 blue, 3 red and 2 green). What is the probability of drawing a blue, setting it aside, and then drawing a green?

  23. Learning together “With replacement” vs. “Without replacement” • Adam has a bag containing four yellow gumdrops and one red gumdrop. he will eat one of the gumdrops, and a few minutes later, he will eat a second gumdrop.a) Draw the tree diagram for the experiment.b) What is the probability that Adam will eat a yellow gumdrop first and a green gumdrop second?c) What is the probability that Adam will eat two yellow gumdrops?d) What is the probability that Adam will eat two gumdrops with the same color? e) What is the probability that Adam will eat two gumdrops of different colors?

  24. assessment • How long do I have? 45 mins • What do I do? By yourself, complete the Unit 5 Common Assessment

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  31. Wrap-up

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