Estimating Probabilities Using Simulation

Warmup

Activity #1

More Experiments on Simulating Probability.

• Read the coin tossing experiment below and answer the questions that follow.

A football referee always used a special coin to toss for ends. She noticed that out of the last twenty matches the coin had come down heads far more often than tails. She wanted to know if the coin was fair, that is, if it was as likely to come down heads as tails.

(1.) Can you help her decide if it is fair or not by clicking on ‘flip’ lots of times?

(2.) If you increase the number of trials, is it a better or worse estimation of the probability?

Activity #2

Calculate Experimental Probabilities by Performing Simulations Involving a Probability Model.

With “Frequency” chosen, start this activity with 1 die, then change to 2 dice, and 3 dice.

• Click “Roll the die 1”. Confirm that the score on the die is displayed on the line. ​
• Note that its frequency is 1.
• Click and click “Roll the die 10”. The display on the graph shows the different outcomes during the ten trials. The numbers at the top are the frequencies, while those below the line are the outcomes on the die.
• Click and click “Roll the die 100”. Confirm that that the numbers at the top add up to 100.
• Click and click “Roll the die 10,000”. The numbers at the top will add up to 10,000.
• Click .
• Now, use the slider use 2 dice. Repeat the steps above.
• Change to 3 dice and also repeat the steps one more time.
• Change to relative frequency and repeat the steps above.

Challenge #1

The weather forecast says there is a 75% chance it will rain later today. Draw a spinner you could use to simulate this probability.

Describe another way you could simulate this probability.

Challenge #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?

Challenge #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.

Quiz Time