Lesson 6
Estimating Probabilities Using Simulation
Problem 1
The weather forecast says there is a 75% chance it will rain later today.
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Draw a spinner you could use to simulate this probability.
- Describe another way you could simulate this probability.
Solution
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Problem 2
An experiment will produce one of ten different outcomes with equal probability for each. Why would using a standard number cube to simulate the experiment be a bad choice?
Solution
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Problem 3
An ice cream shop offers 40 different flavors. To simulate the most commonly chosen flavor, you could write the name of each flavor on a piece of paper and put it in a bag. Draw from the bag 100 times, and see which flavor is chosen the most. This simulation is not a good way to figure out the most-commonly chosen flavor. Explain why.
Solution
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Problem 4
Each set of three numbers represents the lengths, in units, of the sides of a triangle. Which set can not be used to make a triangle?
7, 6, 14
4, 4, 4
6, 6, 2
7, 8,13
Solution
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(From Unit 7, Lesson 7.)Problem 5
There is a proportional relationship between a volume measured in cups and the same volume measured in tablespoons. 48 tablespoons is equivalent to 3 cups, as shown in the graph.
![A point plotted in the coordinate plane with the origin labeled “O”.](https://cms-im.s3.amazonaws.com/wa7PRwbr4eXLBUsLGBmLtGD7?response-content-disposition=inline%3B%20filename%3D%227-7.2.F.PP.Image.05.png%22%3B%20filename%2A%3DUTF-8%27%277-7.2.F.PP.Image.05.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T171908Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=94494c130eb107a8b25e2a71b2e7c24e82b9cf6d518926c08b5235aed538c404)
- Plot and label some more points that represent the relationship.
- Use a straightedge to draw a line that represents this proportional relationship.
- For which value \(y\) is (\(1, y\)) on the line you just drew?
- What is the constant of proportionality for this relationship?
- Write an equation representing this relationship. Use \(c\) for cups and \(t\) for tablespoons.
Solution
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(From Unit 2, Lesson 14.)