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What Do You Expect?

Day Topic Homework IXL Grade 1 Experimental Probability (Inv 1.1) Worksheet 1 2 More Experimental Probabilities Worksheet 2 and read page 27! DD.1 3 Theoretical probability (2.1) Worksheet 3 DD.2 4 Probability Properties (2.2) Worksheet 4 DD.3 5 M&M Game Worksheet 5 DD.4 6 Tree Diagrams Worksheet 6 DD.5 7 Compound Events Study for quiz! DD.6 8 Quiz Worksheet 7 DD.7 9 Models for Sample Space (4.1) Worksheet 8 DD.10

10 Areas Models and Probability(4.2) Worksheet 9 11 More probability situations (4.3) Worksheet 10 12 Practice Review Packet 13 Review day Study for Test 14 Unit Test Be sure IXL is complete

Quiz Date: Wednesday, 2/1 Test Date: Friday, 2/10

Name: ______________________________________________________

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Important Concepts to Remember Vocabulary Probability: A number between 0 and 1that describes the likelihood that an outcome will occur Experimental probability: A probability determined through experimentation. Equally likely: Two or more events that have the same probability of occurring. Outcomes: A result of an event or action.

Theoretical probability: A probability calculated by examining possible outcomes. Tree Diagrams: A diagram used to determine the number of all possible outcomes in a probability

situation. Sample Space: The set of all possible outcomes in a probability situation. Compound Events: An event consisting of two or more simple events. Expected Value: The mean or average for a situation. Binomial Probability: The probability of getting one of two possible outcomes over many trials.

Formulas

Experimental probability: P(event) = number of times event occurs

total number of trials

Theoretical probability:

P(E) = number of favorable outcomes total number of possible outcomes

1 1/2 0

Probability Scale

Impossible Unlikely Equally Likely to

Occur or Not OccurLikely Certain

1 1/2 0

Probability Scale

Impossible Unlikely Equally Likely to

Occur or Not OccurLikely Certain

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Date_____ Day 1 Inv 1.1 Important Vocabulary: Probability, and Experimental Probability Probability of getting heads formula: Directions: Toss a coin 30 times and record your results in the table below. Day Result

(circle) Number of heads so far

Fraction of Heads so far Percent of heads so far (Expected Probability for heads)

1 H or T 2 H or T 3 H or T 4 H or T 5 H or T 6 H or T 7 H or T 8 H or T 9 H or T 10 H or T 11 H or T 12 H or T 13 H or T 14 H or T 15 H or T 16 H or T 17 H or T 18 H or T 19 H or T 20 H or T 21 H or T 22 H or T 23 H or T 24 H or T 25 H or T 26 H or T 27 H or T 28 H or T 29 H or T 30 H or T

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Combined Class Results Table Number of heads

Total number of heads

Total number of trails

Fraction Percent (Expected probability for heads)

30 60 90 120 150 180 210 240 270

1. As we add more data to the table, what happens to the percent of tosses that are

heads?

2. What was the overall experimental probability of getting heads? 3. Based on our results, if there are 30 days in June, about how many times do you think

Kalvin will eat Cocoa Blast?

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Date_____ Day 2 More experimental Probability Spinner Game Suppose you and your friend are about to play a game using the spinner shown here:

Rules of the game:

1. Decide who will go first.

2. Each person picks a color. Both players cannot pick the same color.

3. Each person takes a turn spinning the spinner and recording what color the spinner stops on. The winner is the person whose

color is the first to happen 10 times.

4. Play the game, and remember to record the color the spinner stops on for each spin.

Number of times Blue Red Green

1

2

3

4

5

6

7

8

9

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Which color do you think will win: Blue, Red or green (circle your answer)

1. Which color was the first to occur 10 times? What fraction of the times did it land on this color?

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Combined Class Data: Mark which color won for each group

Group Blue Red Green

1

2

3

4

5

6

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2. Do you think it makes a difference who goes first to pick a color?

3. Which color would you pick to give you the best chance of winning the game? Why would you pick that

color?

4. Below are three different spinners. On which spinner is the green likely to win, unlikely

to win, and equally likely to win? Explain Why.

Read page 27 for homework! Be able to define theoretical probability!

Spinner A

Green Red

Spinner B

Red

Green

Spinner C

Red

Green

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Date_____ Day 3 Finding Theoretical Probabilities Important Vocabulary: Theoretical Probability A) 1. Keep track of the number of times each color is chosen 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Red Yellow Pink

2. Based on our data, find the experimental probability for each color: What is the formula? P(red)= P(yellow)= P(pink)= B) 1. After counting, we have figured out that there are actually: ____ Red Starburst ____ Yellow Starburst ____ Pink Starburst Use this information to calculate the theoretical probability for each What is the formula? P(red)= P(yellow)= P(pink)=

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2. How do the theoretical probabilities compare to the experimental probabilities? 3. What is the sum of the theoretical probabilities? C) 1. Does each starburst, without regard to color, have the same chance of being chosen? Explain. 2. Does each color starburst have the same chance of being chosen? Explain. 3. When choosing a starburst, is it equally likely that it will be red or pink?

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Date_____ Day 4 Inv 2.2 A) 1. P(yellow)= P(blue)= P(red)= 2. 3. 4. P(not blue)= 5. P(red or yellow)= 6. P(white)= 7. Who is correct? Explain.

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B) 1. 2. C) 1. 2. 3. 4.

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Date_____ Day 5 M & M Game:

1 2 3 4 5 6 7 8 9 10 11 12

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Data table: Sum Number of times it occurred 1 2 3 4 5 6 7 8 9 10 11 12

1. Which sum occurred the most? 2. Which sums did not occur very often? 3. What do you think is a good strategy for placing your M&M’s on the board? 4. Find all the possible pairs of numbers you can get from rolling two dice:

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4. Find the sum for each of these outcomes: 5. Using question 4, are all of the sums equally likely? Explain. 6. How many ways can you get a sum of 2? 7. How many ways can you get a sum of 7? 8. How many ways can you get a sum of 7? 9. Which sums occur most frequently? 10. If we were to play the game again, would you have a different strategy? Explain why

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Date_____ Day 6 Tree Diagrams Important Vocabulary: Tree diagrams and Sample Space Example of a tree Diagram: What is the sample space for this tree diagram? What is the probability of choosing pancakes on both days?

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Jamie is at the ice cream standing and trying to figure out the amount of options that she can choose from. First Jamie must decide if she wants her ice cream in a dish or a waffle cone, and then she must choose between vanilla, strawberry or chocolate ice cream. Draw a tree diagram to represent the possibilities Jamie can choose. What is the sample space for ice cream choices? How many possible outcomes are there when choosing ice cream? _____ Are the outcomes equally likely? Yes or No (circle) What is the theoretical probability that Jamie will choose vanilla ice cream? What is the theoretical probability that Jamie will choose chocolate or strawberry? What is the theoretical probability that Jamie will choose a waffle cone? Suppose Jamie was going to buy 6 ice cream cones. How many times would you expect Jamie to buy vanilla?

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Date_____ Day 7 Compound Events Important Vocabulary: Compound Events Jamie just realized the Ice Cream Parlor offers sprinkles. First Jamie must decide if she wants her ice cream in a dish or a waffle cone, and then she must choose between

vanilla, strawberry or chocolate ice cream. Then Jamie must decide if she wants sprinkles or no sprinkles. Draw a tree diagram to represent the possibilities Jamie can choose.

How many options does Jamie have? _______

Example of a Compound Event On the weekends I either eat pancakes or eggs for breakfast. There is a .75 chance on a given day that I will pick pancakes and a .25 chance on a given day that I will pick

pancakes. Draw the tree diagram to represent my possible outcomes.

What is the theoretical probability of choosing eggs on both days?

What is the theoretical probability of choosing pancakes on both days?

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It is now Monday and once again I am going to have pancakes or eggs. There is still a .75 chance I will pick eggs and a .25 chance I will pick pancakes! Draw a new tree diagram

representing my choices.

What is the probability I will eat pancakes all three days?

What is the probability that I will eat pancakes the first two days and eggs the last day?

Reminder: Day 8 is a QUIZ! Study hard

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Date_____ Day 9 Inv 4.1 A) 1. 2.

3. Label each section. B) 1. a. RR b. RB c. RG d. RY e. GR f. GB g. GG h. GY i. YY 2. a.

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b. c. d. C) 1. 4.

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Date_____ Day 10 Inv 4.2 A) Results: Experimental probability: B) Construct an area model

What is the theoretical probability that a player will make purple? Construct a tree diagram to represent the spinners: What is the theoretical probability that a player will make purple?

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C) D) 1. 2. 3. 4. 5.

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Date_____ Day 11 Inv 4.3 A) 1) 2) B) First draw a tree diagram representing the situation: 1) P(0 points)= P(1 point)= P(2 points)=

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3) C) For homework read page 78 and come up with a definition of expected value in your own words. Expected value: