Lesson 5.2.1 – Teacher Notes Standard: 7.SP.C.7a Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. Full mastery of the standard can be expected by the end of the chapter. Lesson Focus: The focus of the lesson is mainly a review of probability from chapter 1 and extending the student’s understanding by challenging students justify probabilities. (5-26 and 5-27) I can develop a uniform probability model and use it to determine the probability of each outcome/event. Calculator: Yes Literacy/Teaching Strategy: Think-Pair-Share (5-25); Listening Post (closure)

Bell Work

Have you ever played a game where everyone should have an equal chance of winning, but one person seems to have all the luck?  Did it make you wonder if the game was fair?  Sometimes random events just happen to work out in one player’s favor, such as flipping a coin that happens to come up heads four times in a row.  But it is also possible that games can be set up to give an advantage to one player over another.  If there is an equal chance for each player to win a game, then it is considered to be a fair game.  If it is not equally likely for each player to win, a game is considered to be unfair. In this lesson you will continue to investigate probability.  As you work, ask these questions in your study team: How many outcomes are possible? How many outcomes are desirable?

Each deck has 4 suits and contains 52 cards total: Clubs, Hearts, Spades, and Diamonds. Each ‘suit’ has 13 cards (10 regular cards and 3 face cards).

5-23. PICK A CARD, ANY CARD What is the probability of picking the following cards from the deck?  Write your response as a fraction, as a decimal, and as a percent.  a. P(black)?  b. P(club)?  c. If you drew a card from the deck and then replaced it, and if you repeated this 100 times, about how many times would you expect to draw a face card (king, queen, or jack)?  Explain your reasoning. 

5-24. Sometimes it is easier to figure out the probability that something will not happen than the probability that it will happen.  When finding the probability that something will not happen, you are finding the probability of the complement.  Everything in the sample space that is not in the event is in the complement. a. What is the probability you do not get a club, written P(not club)?   b. What is P(not face card)?   c. What would happen to the probability of getting an ace on a second draw if you draw an ace on the first draw and do not return it to the deck?  Justify your answer.

5-26. The city has created a new contest to raise funds for a big Fourth of July fireworks celebration.  People buy tickets and scratch off a special section on the ticket to reveal whether they have won a prize.  One out of every five people who play get a free entry in a raffle.  Two out of every fifteen people who play win a small cash prize. a. If you buy a scratch-off ticket, is it more likely that you will win a free raffle ticket or a cash prize?  Explain your answer.   b. What is the probability that you will win something (either a free raffle entry or a cash prize)?  c. What is the probability that you will win nothing at all?  To justify your thinking, write an expression to find the complement of winning something.  

5-27. Alicia’s favorite candies are Fruiti Tutti Chews, which come in three flavors: Killer Kiwi, Crazy Coconut, and Ridiculous Raspberry.  This year will be the 50th year that the candy has been made.  To celebrate, the company that makes Fruiti Tutti Chews is running new advertisements and introducing a fourth flavor: Perfect Peach. a. One of the new advertisements states that if you reach into any bag of Fruiti Tutti Chews, you have a  2 3  probability of pulling out a Killer Kiwi candy.  Another advertisement says that   3 5  of each bag is Ridiculous Raspberry.  Are the advertisements telling the truth?      

5-27 cont. b. Alicia learns that when she opens a new bag of candy, she has a  2 5  chance of pulling out a piece of Ridiculous Raspberry and a  1 3  chance of pulling out a piece of Killer Kiwi.  Could she have a  4 15  chance of pulling out a piece of Perfect Peach?  Explain your reasoning.  c. When the company introduces the new flavor, it plans to make Perfect Peach  3 10  of the candy in each bag.  If there is an equal amount of the remaining three flavors, what is the probability that the first piece you pull out of the bag will be Crazy Coconut?  Justify your answer.

Vocabulary: Probability– expressed as a ratio describing the # of ___________________ outcomes to the # of _______________ outcomes. Probability is measured on a scale from 0 – 1. Theoretical Probability– the probability, based on ______________________, that an event will occur (what should happen). Experimental Probability– found using outcomes obtained in an actual _________________ or game (what actually happens). What SHOULD happen v. What ACTUALLY happens!

Where would the following fall on the above Number Line??? Impossible Unlikely Equally Likely Certain Likely 𝟏 𝟐 Where would the following fall on the above Number Line??? Your parents will win a lottery 6) You will roll a “2” on a standard jackpot this year. number cube. 2) Food will be served for lunch. 7) On your way to school, you will see 3) You will get tails when you flip a coin. a live woolly mammoth drive a van. You will have 2 birthdays this year. 8) The sun will rise tomorrow. You will see a cat this evening. 9) You will see a wild, living black bear in class 10) You will become famous one day.

THEORETICAL AND EXPERIMENTAL PROBABILITY The probability of an event is a number between 0 and 1 that indicates the likelihood the event will occur. There are two types of probability: theoretical and experimental.

Experimental vs. Theoretical Experimental probability: when you do the experiment. P(event) = total number of trials Theoretical probability: what should happen in an ideal situation. P(E) = total number of possible outcomes number of times event occurs number of favorable outcome

What is the Theoretical Probability of: P( red or purple) = P(Green) = P( Purple)= P(Blue) = P(Yellow)= P(Orange) = P( Red) = What is the Theoretical Probability of: P( red or purple) = P( Not Green)= P(Not blue,red or yellow)=

What is the P( getting an act) = What is the P(jack or a number less than 8) = What is the P(face card or red ace) = What is the P(even number or black king) = What is the P(an ace or red face card) =

Mutually Exclusive mutually exclusive events cannot occur at the same time. This means they do not share any outcomes.  https://www.youtube.com/watch?v=SQLAWVkFk4E

Mutually Exclusive mutually exclusive events if they cannot occur at the same time. This means they do not share any outcomes. 

Mutually Exclusive????? 1. 2.

Mutually Exclusive????? 3. 4. P(college degree and work experience) P(Chocolate green Bean & green Jelly bean) 4.

When asked to determine the P(# or #) Mutually Exclusive Events Mutually exclusive events cannot occur at the same time. Answer Yes or No. Draw ace of spaces and then a king of hearts? Draw ace and then a king? Draw a spade and then drawing an ace ?

Addition Rule for Mutually Exclusive Events Add probabilities of individual events Drawing ace of spades or king of hearts Probability of ace of spades is Probability of king of hearts is Probability of either ace of spades or king of hearts is

Drawing a spade or drawing an ace Probability of drawing a spade: Probability of drawing an ace: Ace of spades is common to both events, probability is Is this Mutually exclusive?

mutually exclusive events cannot occur at the same time mutually exclusive events cannot occur at the same time. This means they do not share any outcomes.  What do you think Non-mutually exclusive would be like? 

Independent Practice

5.2.1 Exit Ticket: Name ____________________ Date______ Pd ____