Materials 1.2.1A Resource Page Coloring utensils Small paper clips

Skill Review Alec bought 35 feet of window trim at a hardware store. The trim cost $1.75 per foot, including tax. If Alex paid with a $100.00 bill, how much change should he have received? $20.00 c. 61.25 $38.75 d. 80.00

You have probably heard a weather forecaster say that the chance of rain tomorrow is 40%.  Have you thought about what that means?  Does it mean that it will rain tomorrow for sure?  What is the chance that it will not rain?  In today’s lesson, you will investigate the chance, or the probability, of something happening or not happening.  As you do the activities, ask yourslef these questions: What is the probability of the event occurring? How can we record that probability?

1-50. POSSIBLE OR IMPOSSIBLE? Make lists of three different types of events: Events that you think are possible but not certain to happen, Events that certain to happen. Events that would be impossible to happen.  Complete the activities below: a. On the line segment label the left end “Impossible” and the right end “Certain.” b. At the “Impossible” end, write an event that we decided could not happen.  How could you label the possibility of these events occurring with a percentage? 

1-50. POSSIBLE OR IMPOSSIBLE? Then we will use our lists to complete the activities below: c. At the “Certain” end, write an event that we decided is certain to happen.  How could you label the possibility of these events occurring with a percentage?    d. Along the line, write the events that you thought were possible.  Place them along the line in order from closer to impossible, somewhere in the middle, or closer to certain.

1-51. GO FISH Mike wants to win a giant stuffed animal at the carnival.  He decided to play the “Go Fish” game, which has three prizes: a giant stuffed animal, a smaller stuffed animal, and a plastic kazoo.  The game is set up with a tank containing 1 green fish, 3 blue fish, and 6 yellow fish. The game is set up so that every time a player goes fishing, he or she will catch a fish. a. If all of the fish in the tank are green, how would you describe the probability of Mike’s winning a giant stuffed animal?    

1-51. GO FISH b. The way the tank is set up (with 1 green, 3 blue, and 6 yellow fish), what are the chances that Mike will catch a black fish?  c. Given the information in the problem, what percent of the time would you expect Mike to catch a green fish and win the giant stuffed animal?  Be ready to explain your thinking. 

1-52.  You could expect Mike to win a giant stuffed animal 10% of the time.  A percentage is one way to express the probability that a specific event will happen.  You might also have said you expected Mike to win 1 out of every 10 attempts.  So the probability that Mike will win is   , because the 1 represents the number of desired outcomes (green fish that Mike can catch) and the 10 represents the number of possible outcomes (all the fish that Mike could catch). a. What is the probability that Mike will catch a blue fish? A green fish? A yellow fish?  Write each of these probabilities as a fraction and a percent.  b. Probabilities such as the ones you found in part (a) are called theoretical probabilities because they are calculated mathematically based on what is expected.   Place each fishes probability on the line of probability in problem 1-50

The rest should be green. 1-54. SPINNERS – THEORY vs. REALITY, Part One You will need to decide how to color the spinner so that it meets the following criteria: a. Which color is the most likely result of a spin?  Why?  b. Which color is the least likely result of a spin?  Why?  c. Determine the theoretical probability of the spinner landing on each of the four colors (red, yellow, blue, and green).  Express your answers as fractions and percents.    d. What is the probability of the spinner landing on purple?  Explain.  e. What is the probability of the spinner landing on either red or blue?  40%  should be red. should be yellow. 30% should be blue.  The rest should be green.

1-55. SPINNERS – THEORY vs. REALITY, Part Two Now you will use your new spinner to do an investigation. a. Each person should spin the spinner 10 times and record the color resulting from each spin.  b. Write the number of times the spinner landed on each color as the numerator of a fraction with the total number of spins as the denominator.  c. Now combine your data with the results from the rest of your classmates.  Use the class data to write similar fractions as you did in part (b) for each color.  

1-55. SPINNERS – THEORY vs. REALITY, Part 2 d. Recall that the numbers you calculated in part (c) of problem 1-54 are theoretical probabilities, because you calculated these numbers (before actually spinning the spinner) to predict what you expected to happen.  The numbers you found in your investigation (when you actually spun the spinner) are called experimental probabilities, because they are based on the results from an actual experiment or event.  Both theoretical and experimental probabilities can be written as a percent, a fraction, or a decimal. i. Does it make sense that the theoretical probabilities and the experimental probabilities you calculated for the spinner might be different? Explain. ii. Does it make sense that the experimental probabilities that you found for the class are different from those found for just your team?

Practice

A bag contains 10 red marbles, 8 blue marbles and 2 yellow marbles. Lesson 1.2.1 Prep 7.SP.6 A bag contains 10 red marbles, 8 blue marbles and 2 yellow marbles. Find the probability for each event below. Write your answer as a fraction, decimal, and percent. P(blue) = P(red) = P(yellow) = P(red or blue) = Answer: P(blue) = 𝟖 𝟐𝟎 0.4 40% P(red) = 𝟏𝟎 𝟐𝟎 0.5 50% P(yellow) = 𝟐 𝟐𝟎 0.1 40% P(red or blue) = 𝟏𝟖 𝟐𝟎 0.9 90%