# Lesson 7

Simulating Multi-step Experiments

Let’s simulate more complicated events.

### Problem 1

Priya’s cat is pregnant with a litter of 5 kittens. Each kitten has a 30% chance of being chocolate brown. Priya wants to know the probability that at least two of the kittens will be chocolate brown.

To simulate this, Priya put 3 white cubes and 7 green cubes in a bag. For each trial, Priya pulled out and returned a cube 5 times. Priya conducted 12 trials.

Here is a table with the results.

trial number outcome
1 ggggg
2 gggwg
3 wgwgw
4 gwggg
5 gggwg
6 wwggg
7 gwggg
8 ggwgw
9 wwwgg
10 ggggw
11 wggwg
12 gggwg
1. How many successful trials were there? Describe how you determined if a trial was a success.

2. Based on this simulation, estimate the probability that exactly two kittens will be chocolate brown.
3. Based on this simulation, estimate the probability that at least two kittens will be chocolate brown.
4. Write and answer another question Priya could answer using this simulation.

5. How could Priya increase the accuracy of the simulation?

### Problem 2

A team has a 75% chance to win each of the 3 games they will play this week. Clare simulates the week of games by putting 4 pieces of paper in a bag, 3 labeled “win” and 1 labeled “lose.” She draws a paper, writes down the result, then replaces the paper and repeats the process two more times. Clare gets the result: win, win, lose. What can Clare do to estimate the probability the team will win at least 2 games?

### Problem 3

1. List the sample space for selecting a letter a random from the word “PINEAPPLE.”
2. A letter is randomly selected from the word “PINEAPPLE.” Which is more likely, selecting “E” or selecting “P?” Explain your reasoning.
(From Unit 8, Lesson 5.)

### Problem 4

On a graph of side length of a square vs. its perimeter, a few points are plotted.