# Lesson 9

Multi-step Experiments

### Problem 1

A vending machine has 5 colors (white, red, green, blue, and yellow) of gumballs and an equal chance of dispensing each. A second machine has 4 different animal-shaped rubber bands (lion, elephant, horse, and alligator) and an equal chance of dispensing each. If you buy one item from each machine, what is the probability of getting a yellow gumball and a lion band?

### Solution

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### Problem 2

The numbers 1 through 10 are put in one bag. The numbers 5 through 14 are put in another bag. When you pick one number from each bag, what is the probability you get the same number?

### Solution

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### Problem 3

When rolling 3 standard number cubes, the probability of getting all three numbers to match is $$\frac{6}{216}$$. What is the probability that the three numbers do not all match? Explain your reasoning.

### Solution

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### Problem 4

For each event, write the sample space and tell how many outcomes there are.

1. Roll a standard number cube. Then flip a quarter.

2. Select a month. Then select 2020 or 2025.

### Solution

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(From Unit 8, Lesson 8.)

### Problem 5

On a graph of the area of a square vs. its perimeter, a few points are plotted.

1. Add some more ordered pairs to the graph.
2. Is there a proportional relationship between the area and perimeter of a square? Explain how you know.

### Solution

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(From Unit 2, Lesson 11.)