Lesson 2

Explore

 

In Discover you constructed a sample space table of all possible outcomes. This table can be used to determine the theoretical probability of the different outcomes.

 

Theoretical probability is determined by calculating the number of favourable outcomes and the total number of possible outcomes, whereas experimental probability is determined by performing an experiment, as you did in Lesson 1 of this module.

 

The formula for calculating theoretical probability is the same as experimental probability.

 

Source: MathWorks 12 Student Book/Teacher Guide. (Vancouver:Pacific Educational Press, 2011.)

 

	Experimental Probability	Theoretical Probability
Definition	the ratio of the number of occurrences of a particular event during an experiment or trial to the total number of trials conducted	the ratio of one or more events of interest to the total number of possible outcomes
Formula

 

For example, when flipping a single coin, the result will be either heads or tails. There are only two possible outcomes.

 

The theoretical probability of flipping a head is

 

In Try This 3 you will further explore how theoretical probability and experimental probability compare.

 

Try This 3

 

Predict how many heads will appear when 16 coins are flipped. Does your prediction change if there are 32, 48, or 64 coins flipped? Test your prediction with an experiment.

 

Open Coin Flipper and click on 16 for the number of coins. Then select “Flip Coins.” Note that this experiment can also be completed using a real coin by simply flipping it 16 times, and recording the results. You can also flip 16 coins at once.

 

coin images: Royal Canadian Mint. All Rights Reserved.

 

Predict the number of heads you expect for each of the next four trials of 16 coins, and record your predictions in a table similar to the one that follows.

 

	Cumulative Number of Coins Flipped	Predicted Number of Heads	Actual Number of Heads
1st set of 16 coins
2nd set of 16 coins
3rd set of 16 coins
4th set of 16 coins
5th set of 16 coins
Total

 

Flip the coins four more times, for a total of five 16-coin trials.

 

Record in the table the total number of heads that appear.

 

Save your responses in your course folder.

 

Share 2

 

With a partner or in a group, discuss your findings from Try This 3. Then use your results to answer the following questions.

1. Combine your results. Determine the total number of flips of the coin. Determine the total number of heads that appeared. What is the experimental probability of flipping a head based on the combined data?
2. Calculate the theoretical probability of flipping a head. Are the two probabilities close?
3. How do you think these numbers would compare if you flipped 10 times as many coins?

If you wish, find more people to add to your group and combine the results. Are your findings closer to the theoretical probability?

 

Save your responses in your course folder.