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3 Station #1: M & M s 1. What is the sample space of your bag of M&M s? 2. Find the theoretical probability of the M&M s in your bag. Then, place the candy back into the bag, pull out an M&M and record the results under experimental probability. Repeat for a total of 20 times. Candy Color Theoretical Probability Total # of each color in bag Color Total % color in your bag Tally Marks- 20 times Experimental Probability Color Picked 20 tries % Red Blue Yellow Green Brown Orange 3. Is the experimental probability of the colors you picked in the 20 tries equal to the theoretical probability found in the bag? Why or why not? 4. P(choosing a yellow without replacing it & then a blue) 5. P(choosing a yellow or a brown) 3
4 Station #2: Money Toss 1. Take 2 coins, a penny and a nickel, and predict all the possible outcomes that can occur when you toss the 2 coins. Record your results in the table below. Find the theoretical probability for each outcome. Theoretical Probability Outcome Penny Nickel Fraction Percent Toss both coins 20 times and record your results in the table below. (Tails/ Heads) Event Penny Nickel Event Penny Nickel Use the information in # 1 & #2 above to complete the table below. Theoretical Probability Experimental Probability Event Fraction Percent Fraction Percent Both coins are heads At least one coin falls tails One head and one tail 4
5 3. Write a complete sentence comparing the experimental probability and the theoretical probability. Station #3: M & M s in a Bag Using the M & M clue cards on the website agenda, determine how many colors of each M & Ms there are in the bag. Brown: Blue: Green: Orange: Yellow: Station #4: Draw the Spinner Using the spinner clues on the website agenda, draw what the spinner would look like. Draw spinner 1 first and then draw spinner 2. 5
6 Station #5: Deck of Cards: Ace (1), 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack (11), Queen (12), King (13) Clubs: Diamonds: Spades: Hearts: 1. Take a standard deck of cards containing 52 cards and determine the theoretical probability of picking the following cards. Theoretical Probability Event Fraction Percent Event Fraction Percent Ace of Spades A Numbered Card A Red Card A Queen A Red or Black Card Jack of Hearts Not a Red or Black Card Two of Clubs A Heart or a Diamond An Ace or a King Not a Club A Seven, Eight or Nine Not a Face Card Queen of Diamonds A Two, Three, Four or Five A Prime Numbered Card 2. Randomly, pick a card 20 times (replacing the card each time) and record your results. This is your experimental data. Use initials for your data (ie. KS is King of Spades). Spades (S), Clubs (C), Hearts (H), Diamonds (D) Event Card Event Card Event Card Event Card
7 3. Experimental Probability- Record your results from page 6 in the chart below. Event Fraction Percent Event Fraction Percent Ace of Spades A Heart or a Diamond A Numbered Card An Ace or a King A Red Card Not a Club A Queen A Red or Black Card Jack of Hearts Not a Red or Black Card Two of Clubs A Seven, Eight or Nine Not a Face Card Queen of Diamonds A Two, Three, Four or Five A Prime Numbered Card 4. Compare the theoretical results with the experimental results from the two charts above. Explain your findings. Station #6: Spinners- Use the spinner link on the website agenda. Spinner #1: This spinner has 3 red, 3 blue, and 2 green regions. 1. Spin the spinner 10 times and record your results below. Event Color Event Color
8 2. The pointer is equally likely to stop on any of the spaces. Find the theoretical probability (TP) and experimental probability (EP) from the above data of each of the following: Event a blue region Theoretical Experimental Fraction % Fraction % a green region a red region a non-blue region a non-green region Spinner #2: This spinner has 4 brown, 2 yellow, 3 purple, and 3 orange spaces. 3. Spin the spinner 10 times and record your results. Event Color Event Color Find the theoretical probability (TP) and experimental probability (EP) from the above data of each of the following: Theoretical (TP) Experimental (EP) Event Fraction % Fraction % a brown region a purple region a yellow or orange region a non-yellow region a non-purple region 5. Write a complete sentence comparing the experimental probability and the theoretical probability. 8
9 Station #7: Dice Toss 1. The list shown lists all the possibilities when rolling 2 six-sided number cubes. (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) 2. How many different possibilities are there when rolling 2 six-sided number cubes? 3. Complete the addition chart. List all of the theoretical probabilities that can occur when rolling two dice and record below Using the chart above, write the theoretical probability as a fraction and then as a percent for each number. Probability Fraction Percent Probability Fraction Percent P(1) P(7) P(2) P(3) P(4) P(5) P(6) P(8) P(9) P(10) P(11) P(12) 9
10 5. Is there an equally likely chance for each number to result from rolling 2 six-sided number cubes according to the theoretical probabilities? 6. If the number cubes are tossed 180 times, how many times do you predict the following sums would occur? Outcome Theoretical Probability Prediction / Prime Number Composite Number 7. Throw a pair of dice 50 times. Add the two dice and record with tally marks below to find the experimental probability. Then find the fraction & percent out of the 50 rolls. Sum # of rolls Fraction Percent Sum # of rolls Fraction Percent Which sum is impossible? Which sum occurs most often? Which sum occurs least often? 10
11 8. Make a line plot for the theoretical & experimental probability of the sum outcomes of the dice rolls. Make a key & assign a different color to the theoretical & experimental results. 9. How does the experimental probability compare to the theoretical probability? Explain your findings. Station #8: Probability and Your Class Jarek Sophie Felipe Justice Leo Lexxie Zach Paige Jenna Olivia Mano Hailey Sean Stephanie Darin Keira Luke Maddie Andrea Pablo Jack Cassie Michael Alex Use the class list to determine the probabilities of the following events. Suppose that each of these names were written on a card and the cards were shuffled and kept facedown. What are the chances of drawing classmates name with? 1.) The first letter being D? 2.) A five letter name? 3.) A name in which the first letter is a vowel? 11
12 4.) Double letters that are adjacent? (Ex. Annie) 5.) The letter a somewhere in their name? 6.) A name that contains more than 4 vowels? 7.) A name that contains three or more syllables? 8.) A name that has the total number of letters equaling a prime number? 9.) A name that begins and ends with the same letter? 10.) A name with seven or more letters? 11.) How many total letters do you think there are in all the names? Estimate: Actual: 12.) What is the probability that a girl will be chosen first, not replaced and another girl will be chosen? Show your work. 13.) What is the probability that a girl will be chosen first, replaced and a boy will be chosen second? Show your work. 14.) What is the probability that a girl will be chosen first, not replaced and then a boy will be chosen? Show your work. 15.) What is the probability that a person s name starting with a vowel will be chosen, not replaced and then another person s name starting with a vowel will be chosen? Show your work. 16.) What is the probability that a name starting with the letter A will be chosen, replaced, and then the letter T? Show your work. 17.) What is the probability that a name starting with the letter M will be chosen, not replaced and another M will be chosen? Show your work. 12
13 Station #9: Rock, Paper, Scissors 1. What is the theoretical probability of getting rock, paper, and scissors? 2. With a partner, play this game 30 times and fill out the table to record the results that represent experimental probability. Each time you make a move, record which outcome you made. If the outcome was a win, write a tally in the wins category for rock, paper, scissors that made the win. Circle which player # you represent. Keep track in your own packet. Player #1 #2 Result Tallies/ 30 Number of Wins Total Outcomes as a Fraction Percentage 3. How did the theoretical probability & the experimental probability compare? 13
14 Station #10: Tossing Cups 1. Find the theoretical probability of the tossing the cup and it landing on its end and side. Station #10: Tossing Cups Cup Landing Position End Theoretical Probability Fraction Percent Side 2. The game is played between two players. To play the game, cup is tossed in the air. Play the game 25 times with a partner. Decide who will be Player 1 and who will be Player 2. Record your results in the table using tally marks. Then, write your and your opponent s total score, and write the number of times the cup landed on its side. Calculate the fraction, percent and total points. Tossing Paper Cups Experimental Probability Cup Landing Position Tallies / 25 Fraction Percent Total Points Player #1 0 Points Side Player #2 End 3. Do you think this is a fair game to play? Why or why not? 4. When you toss a six-sided number cube, the probability of it landing on any of the numbers from 1 through 6 is 1. Is it possible to determine the exact probability of the 6 cup landing on its top, bottom, or side? Explain your reasoning. 14
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Name: Per: What Do You Expect Unit (WDYE): Probability and Expected Value Investigations 1 & 2: A First Look at Chance and Experimental and Theoretical Probability Date Learning Target/s Classwork Homework
e. Are the probabilities you found in parts (a)-(f) experimental probabilities or theoretical probabilities? Explain.
1. Josh is playing golf. He has 3 white golf balls, 4 yellow golf balls, and 1 red golf ball in his golf bag. At the first hole, he randomly draws a ball from his bag. a. What is the probability he draws
Applications. 28 How Likely Is It? P(green) = 7 P(yellow) = 7 P(red) = 7. P(green) = 7 P(purple) = 7 P(orange) = 7 P(yellow) = 7
Applications. A bucket contains one green block, one red block, and two yellow blocks. You choose one block from the bucket. a. Find the theoretical probability that you will choose each color. P(green)
* How many total outcomes are there if you are rolling two dice? (this is assuming that the dice are different, i.e. 1, 6 isn t the same as a 6, 1)
Compound probability and predictions Objective: Student will learn counting techniques * Go over HW -Review counting tree -All possible outcomes is called a sample space Go through Problem on P. 12, #2
Probability Essential Math 12 Mr. Morin
Probability Essential Math 12 Mr. Morin Name: Slot: Introduction Probability and Odds Single Event Probability and Odds Two and Multiple Event Experimental and Theoretical Probability Expected Value (Expected
Unit 19 Probability Review
. What is sample space? All possible outcomes Unit 9 Probability Review 9. I can use the Fundamental Counting Principle to count the number of ways an event can happen. 2. What is the difference between
Unit 6: Probability Summative Assessment. 2. The probability of a given event can be represented as a ratio between what two numbers?
Math 7 Unit 6: Probability Summative Assessment Name Date Knowledge and Understanding 1. Explain the difference between theoretical and experimental probability. 2. The probability of a given event can
#2. A coin is tossed 40 times and lands on heads 21 times. What is the experimental probability of the coin landing on tails?
1 Pre-AP Geometry Chapter 14 Test Review Standards/Goals: A.1.f.: I can find the probability of a simple event. F.1.c.: I can use area to solve problems involving geometric probability. S.CP.1: I can define
A prime number = Player X wins. An even number = Player X wins. A number not divisible by three = Player X wins RANDOM NUMBER GENERATOR
If you toss a coin ten times, what is the probability of getting three or more heads in a row? If an airline overbooks a certain flight, what is the chance more passengers show up than the airplane has
Diamond ( ) (Black coloured) (Black coloured) (Red coloured) ILLUSTRATIVE EXAMPLES
CHAPTER 15 PROBABILITY Points to Remember : 1. In the experimental approach to probability, we find the probability of the occurence of an event by actually performing the experiment a number of times
Chance and Probability
G Student Book Name Series G Contents Topic Chance and probability (pp. ) probability scale using samples to predict probability tree diagrams chance experiments using tables location, location apply lucky
(a) Suppose you flip a coin and roll a die. Are the events obtain a head and roll a 5 dependent or independent events?
Unit 6 Probability Name: Date: Hour: Multiplication Rule of Probability By the end of this lesson, you will be able to Understand Independence Use the Multiplication Rule for independent events Independent