Lesson 5 2 1 Teacher Notes Standard 7

Lesson 5. 2. 1 – Teacher Notes Standard: 7. SP. C. 7 a 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. a) 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)

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)? 0. 5 50% 0. 25 25% 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. X = 23

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.

Vocabulary: favorable Probability– expressed as a ratio describing the # of __________ total outcomes to the # of ________ outcomes. Probability is measured on a scale from 0 – 1. what we know that Theoretical Probability– the probability, based on ___________, an event will occur (what should happen). Experimental Probability– found using outcomes obtained in an actual experiment _________ or game (what actually happens). What SHOULD happen v. What ACTUALLY happens!

Impossible 0 Equally Likely Certain Likely Unlikely Where would the following fall on the above Number Line? ? ? 1) Your parents will win a lottery jackpot this year. Unlikely 6) You will roll a “ 2” on a standard number cube. Unlikely 2) Food will be served for lunch. 7) On your way to school, you will see Certain 3) You will get tails when you flip a coin. Equally Likely 4) You will have 2 birthdays this year. Impossible 5) You will see a cat this evening. Equally Likely a live woolly mammoth drive a van. Impossible 8) The sun will rise tomorrow. Certain 9) You will see a wild, living black bear in class Impossible 10) You will become famous one day. Unlikely

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) = number of times event occurs total number of trials Theoretical probability: what should happen in an ideal situation. P(E) = number of favorable outcome total number of possible outcomes

P(Green) = P( Purple)= P(Blue) = P(Orange) = P( Red) = P(Yellow)= 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 ace) = 4/52 What is the P(jack or a number less than 8) = 28/52 What is the P(face card or red ace) = 14/52 What is the P(even number or black king) = 22/52 What is the P(an ace or red face card) = 10/52

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=SQLAWVk. Fk 4 E

Mutually Exclusive e h t t r a mes. u c oc outco t o nn any a c ey share h t f i t s o t n n ve do e y e e siv ans th u l c ex is me y l l tua e. Th u m e tim sam

1. Mutually Exclusive? ? ? 2. Yes! No!

Mutually Exclusive? ? ? 3. P(college degree and work experience) Yes! They do not share any outcomes. 4. P(Chocolate green Bean & green Jelly bean) Yes! They are not the same time.

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? Yes • Draw ace and then a king? Yes • Draw a spade and then drawing an ace ? No

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 1/52 • Probability of king of hearts is 1/52 • Probability of either ace of spades or king of hearts is 2/52

Drawing a spade or drawing an ace • Probability of drawing a spade: 13/52 = ¼ • Probability of drawing an ace: 4/52 = 1/13 • Ace of spades is common to both events, probability is 13/52 + 4/42 – 1/52 = 16/52 = 4/13 Is this Mutually exclusive?

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 ____