Lesson 6

Estimating Probabilities Using Simulation

Problem 1

The weather forecast says there is a 75% chance it will rain later today.

1. Draw a spinner you could use to simulate this probability.

2. Describe another way you could simulate this probability.

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?

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.

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?

A:

7, 6, 14

B:

4, 4, 4

C:

6, 6, 2

D:

7, 8,13

Solution

(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.

1. Plot and label some more points that represent the relationship.
2. Use a straightedge to draw a line that represents this proportional relationship.
3. For which value $$y$$ is ($$1, y$$) on the line you just drew?
4. What is the constant of proportionality for this relationship?
5. Write an equation representing this relationship. Use $$c$$ for cups and $$t$$ for tablespoons.