1. Probability Quizzes and Games Week of April 4-8, 2011 7.14.1: Relate theoretical probability to experimental results

2. Day 1 Warm-Up: Integer Add/Subtract C Collect HW Practice Quiz Correct Practice Quiz Real Quiz Constructed Response on 7.14.1: Relate theoretical probability to experimental results

3. Probability HW cube numbered 1-6 and a coin1. Tyler is performing an experiment using a number cube numbered 1-6 and a coin. He tosses the number cube and flips the coin and records the result. If he performs 60 trials of the experiment, how many times should he expect to toss a number greater than 4 and also have the coin land on heads? Hint: ALWAYS create sample space first. Use it to create first part of proportion. H1 H2 H3 H4 H5 H6 2 = x x=10 times T1 T2 T3 T4 T5 T6 12 60 2. Sanjay is playing a game using a number cube labeled 1 through 6. He rolls the cube 24 times. What is the best prediction for the number of times Sanjay should expect to roll a number greater than 4? Sample Space: 1 2 3 4 5 6 2 = x Proportion: 6 24 x = 8 times 3. Kyle is performing an experiment using a number cube numbered 1-6 and this spinner. He tosses the number cube and spins the spinner. If he performs 120 trials of the experiment, how many times should he expect to toss a number less than 4 and also have the spinner land on purple? Hint: Finish sample space here:Proportion: P1 P2 P3 P4 P5 P6 3 = x R1 R2 R3 R4 R5 R6 24 120 x=15 G1 G2 G3 G4 G5 G6 B1 B2 B3 B4 B5 B6

4. HW Continued 4. Jeremy has a box of colored pushpins. Each pushpin is one of 5 colors: red, blue, green, yellow, and purple. There is an equal number of each color in the box. Jeremy randomly selects a pushpin from the box, records its color, and places it back in the box. Jeremy repeats this experiment 40 times. What is the best prediction for the number of red pushpins Jeremy should expect to get? Sample Space: Proportion: r y g b p 1 = x 5 40 x = 8times 5. Ethan performs an experiment using a coin and this spinner. He tosses the coin and spins the spinner. If he performs 70 trials of the experiment, how many times should he expect to toss a head and also have the spinner land on red? Sample Space: gh gh rh bh bh 1 = x x=7 gt gt rt bt bt 10 70 times

5. Homework Continued… 6. Carrie is playing a game using a number cube with sides labeled 1 through 6. She rolls the cube 36 times. What is the best prediction for the number of times Carrie should expect to roll a number less than 3? Sample Space: 1 2 3 4 5 6 2 = x 6 36 x= 12 times 7. Ian is performing an experiment using two number cubes, each numbered 1-6. He rolls the two number cubes and records the results. If he performs 60 trials of the experiment, how many times should he expect to roll an even number on both cubes at the same time? 1-1 1-2 1-3 1-4 1-5 1-6 2-1 2-2 2-3 2-4 2-5 2-6 9 = x 3-1 3-2 3-3 3-4 3-5 3-6 36 60 60 x 9 = 540 / 36 = 15 times 4-1 4-2 4-3 4-4 4-5 4-6 5-1 5-2 5-3 5-4 5-5 5-6 6-1 6-2 6-3 6-4 6-5 6-6

6. Practice Quiz *Express probability as a fraction, a decimal, and a percent. Do not round. 1. Suppose you roll a die and toss a coin. List all of the possible outcomes: 2. What is the theoretical probability of getting tails and a prime number? 3. Kimberly tested the theoretical probability. She rolled a die and tossed a coin 8 times. Her results are shown below: What is Kimberly’s experimental probability for getting tails and a prime number? 4. How many times would you have expected Kimberly to get tails and a prime number? Why? 1. H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6 2.T2, T3, T5 = 3/12 = 0.25 = 25% 3. Got it only once: T2 =1/8 trials = 0.125 = 12.5% 4. Use proportion. 1 st ratio is from sample space. 3 = x 12 8 attempts We expected her to get it 2 times (cross multiply and divide by 3 rd side)

7. Quiz Time! Put up dividers (no peaking at other’s work) Open note! Hope you all get an A!!!! Good Luck!

8. Constructed Response 7.14.1 Keep dividers up and start your CR Finish for Homework if you did not turn into class. Clean up: Have a great day!

9. Day 2: Let the games begin! Warm-Up: Integer Multiplication C (5 min) Review Probability Project (test grade) Pick partners Create 22 problems on probability with partner (each does 3 theoretical based on your sample space, 3 experimental where you make up the trials testing your sample space, and 5 proportion problems similar to this week’s homework).

10. 20 Probability Problems Draw sample space(s) first!!!!! 2 dice: 1-1 1-2 1-3 1-4 1-5 1-6 2-1 2-2 2-3 2-4 2-5 2-6 3-1 3-2 3-3 3-4 3-5 3-6 4-1 4-2 4-3 4-4 4-5 4-6 5-1 5-2 5-3 5-4 5-5 5-6 6-1 6-2 6-3 6-4 6-5 6-6 Coin and die: H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6

11. Theoretical Problems Each partner will create 3 Theoretical problems based on your sample space. Examples: 1. When you roll 2 dice, what is the theoretical probability of getting a sum of 7? Expess as a fraction in lowest terms. Answer: 6 out of 36 6 36 = 1/6 = 1 out of 6 rolls should be a sum of 7. 2. When you roll a die and flip a coin, what’s the probability of getting a heads and a prime #? Express as a percent. 3 out of 12 = 25% AttemptAttempt

12. Experimental Problems Each partner creates 3 experimental problems like the following: 3 off of 2 dice and 3 off of die and coin. #1 Example: Justin rolled the following numbers. What was his experimental probability of getting a sum of 7? Express as a percent. Answer: 3 out of 8. 3 divided by 8 =.375 = 37.5% # of tries 12345678 Die 163145325 Die 224532163

13. Experimental Problem Coin and Die Example: What is the experimental result of rolling a prime # and a heads? Express as a %. Answer: 3/5 = 60% # tries 12345 Coin HTTHH Die 24335

14. Day 2 Homework: Each partner will create 5 proportion problems based on their sample space (see Day 3 homework from last week for more examples). 2 Dice example: If Lori rolls 2 dice 50 times, how many times would we expect her to get a sum of 7? Answer: 6 = x 36 50 6 x 50 = 300 / 36 = 8.3. We would expect her to get a sum of 7 about 8 times.

15. Probability Proportion Problems Coin and Die Example: If Justin rolled a die and tossed a coin 30 times, how many times would we expect him to get a prime number and heads? Answer: 3 = x 12 30 3 x 30 = 90 divided by 12 = 7.5 We would expect him to roll it 7 or 8 times.

16. Great Class!!! Clean up area (pencil tips up, calculators away, chairs in, wait to be excused). Remember to go online to view examples if you have trouble with your homework!