Course 2, Lesson 1.2.3

HW: 1-80 to 1-84

Learning Target: Scholars will describe what happens to the probability of an event when the sample space is changed by multiplication.

If you want to have the best chances of getting a red gumball from a gumball machine, is it better if the machine is full of gumballs or half empty? How do the chances of getting an ace in a deck of playing cards change if you have three or four decks of cards to choose from instead of only one deck? In this lesson, you will think about the size of the sample space (the collection of all possible outcomes of an event). Think about these questions as you work today:

 How has the “whole” or total changed?

 How has the “portion” or part we are interested in changed?

 Has the event become more or less likely?

1-75.Your team will be given a bag containing a set of colored blocks or counters. Alternatively, use the 1-75 Student eTool(CPM) which contains a bag with 1 yellow, 2 red, 4 green, and 5 blue blocks.Each team will receive a bag that is identical to yours.

Look at the blocks in your bag. If you were to reach into the bag and select one block without looking, what is the likelihood that it would be:
Red?
Green?
Blue?
Orange?
Do your answers for part (a) represent theoretical or experimental probabilities? Justify your response.

1-76.If you were to select one block from the bag 12 times, replacing the block you drew between each selection, how many of those times would you expect to have selected a blue block? What if you drew 24 times? Discuss both situations with your team and explain your answers.

1-77. DOUBLING BAGS

Now imagine that you and another team have combined the blocks from both of your bags into one bag. Explore this concept using the 1-77 Student eTool(CPM) where two bags from 1-75 are combined.

Do you think the larger sample space will change the likelihood of drawing blocks of different colors? Discuss this with your team and be ready to explain your ideas to the class.
Get a second bag of blocks from your teacher and combine the contents of both bags. How many total blocks are there in the bag now? How many are there of each color?
Work with your team to find the theoretical probability for selecting each color of block in the combined bags.
Has the probability for drawing each different-colored block changed? How do your answers for part (c) above compare to the theoretical probabilities that you calculated for the original bag in problem 1-75? With your team, make sense of how the probability for drawing a blue block compares before and after combining the bags.
If you were to make 12 draws from the combined bag, replacing the block between draws, how many times would you expect to draw a blue block? Explainwhy your answer makes sense..

1-78. In problems 1-75 through 1-77, even though you combined bags or changed the number of selections you made, the probability of drawing a blue block remained the same.

Do you think the probabilities would change if you combined three bags? Why or why not?
What change do you think you could make in order to increase the chances of choosing a blue block? Explain your reasoning.

1-80.Tom keeps all of his favorite marbles in a special leather bag. Right now, five red marbles, four blue marbles, and three yellow marbles are in the bag.

If he randomly chooses one marble to give to a friend, what is the probability that it is blue?
Tom does not really want to give away blue marbles and would like to change the probability that he chooses a blue marble to. How many marbles that are not blue could he add to the bag so that the probability of choosing a blue marble becomes?

1-81. Your team is in charge of games at the CPM Amusement Park. One of the games involves a robotic arm that randomly grabs a stuffed animal out of a large bin. Youneed to set up the game so that the probability of acustomer’s grabbing a teddy bear is exactly.

How would you set up the bin? Explain.
What if you returned to check on the bin and found that there were 4 teddy bears left and 12 other animals? What could you add to or remove from the bin to return the probability of selecting a teddy bear to?

1-82.Write four different fractions that are equal to 1. Use your calculator to check that you are correct.

1-83.A rectangular park is 150 yards on one side and 125 yards on the other.

If Debbie walks around the park two times, how far does she walk? Sketch a figure and show your work.
If Debbie wanted to walk 1,000,000 yards, how many times would she have to walk around the park?

1-84. Find the perimeter and area of each figure.

Lesson 1.2.3

1-75. See below:
See below:
0
Theoretical probabilities, they are based on the situation, not data from the experiment.

1-76. About 5 of the 12 draws would be expected to be blue. About 10 of 24 draws are expected to be blue.

1-77. See below:

Answers will vary; Students may think that this doubles the probabilities or makes the chances of selecting some colors greater and the chances of drawing others smaller, but it does not.
24 total blocks. 2 yellow, 4 red, 8green, and 10 blue
P(yellow) =, P(red) =, P(green) =, and P(blue) =
The probabilities are the same; when each color is doubled, so is the total, so the portion sizes remain the same; and are equivalent fractions.
5 times. The probability is still .

1-78. See below:
See Suggested Lesson Activity for possible answers.
See Suggested Lesson Activity for possible answers.

1-79.In the long run, you will end up with negative points.

1-80. See below:
=
28

1-81. See below:
Make sure that half of the stuffed animals are teddy bears.
Possible response: add 8 teddy bears or remove 8 of the other animals.
1-82. Answers vary.

1-83. See below:
1100 yards
Walking around 1818 times would get her 999,900 yards, so she would have to walk around 1819 times.

1-84. See below:
P = 44.85 m, A = 117 m2
P = 30 m, A = 18 m2