Priya, Am, and Tosh had been settling nicely into their new routine when Am suddenly started having frightening symptoms. After many doctor visits and even more tests, Am was diagnosed with Type 1 diabetes.

Priya did an internet search. She typed the question “what is the probability of having type 1 diabetes” into her search engine.

She found this:

She also found this statistic:

Priya was instantly alarmed.

Questions

1. Considering the above statistics, what is the probability that the child of a man who has type 1 diabetes will develop diabetes? Select all that apply.
   a. 1/17
   b. about 0.059
   c. about 59
   d. about 59%
   e. about 5.9%
   f. about 6 out of every 100 people
   g. about 59 out of every hundred people
   h. about 59 out of every thousand people
   
   Answer

   a, b, e, f and h are all correct.
   Probability tells you how likely something is going to happen. It indicates how many times something is expected from a sample of any size. When the sample size is 100, probability is often expressed as a percentage.
   Recognize that "percent" means "out of 100," so 59% means 59 out of 100. Do a quick estimation. Does 1 out of 17 sound about the same as 59 out of 100?
   Does 1 out of 17 sound about the same as 59 out of 100?

Understanding Probability

To better understand what this probability means, you are going to do an investigation. This investigation is designed to give you a more complete understanding of probability by observing data gathered from a virtual spinner.

Learning Goals for the investigation:

• We are learning to compare theoretical probability from experimental probability;
• We are learning to explain why theoretical probability and experimental probability are different.

Success Criteria for the investigation:

• I can determine a theoretical probability;
• I can distinguish theoretical probability from experimental probability;
• I can explain how probability is determined from gathering data.

What is theoretical probability and what is experimental probability?

This spinner from the National Council of Mathematics Teachers is divided into six sections,
so the theoretical probability of the spinner landing on each section is 16.7%.
The experimental probability can only be determined by spinning.

Theoretical probability is based on reasoning rather than collecting data. It is sometimes called "expected probability" because it describes what we intuitively expect to happen. Something is intuitive when you do it without thinking too much about it. You are using your intuition or your feelings, rather than facts or arguments.

Theoretical probability is the ratio of the number of times a particular outcome is expected to occur to the total number of possible outcomes.

Experimental probability is based on actual data collected while doing an activity. To calculate an experimental probability of a particular outcome, you have to track how many times you observe that outcome, as well as how many times you do the activity in total.

Experimental probability is the ratio of the number of times an outcome does occur to the total number of trials or times the activity is performed.

The term "experimental probability" does not necessarily mean that an experiment has been conducted. It means that the probability has been calculated from observed data. Any study that collects data could be used to calculate an "experimental" probability.

Uncertainty

Uncertainty is a part of life. However likely something may be, or however probable it is that something will happen, until it does happen, we cannot be sure. This is uncertainty.

When you did the investigation with the spinner, you observed that the theoretical probability of the spinner landing on blue never changed. It was always 50%. The same was true for the theoretical probability of the spinner landing on yellow.

The prediction that the spinner would land on blue and yellow an equal number of times was not affected by observing what actually happened.

Theoretical probability is the ratio of the number of times a particular outcome is expected to occur to the total number of possible outcomes.

In contrast, the experimental probability changed after every spin. Each time new data was recorded, the counts changed. Either:

• The spinner landed on blue, so the number of blue went up and the number of spins went up

OR

• The spinner landed on yellow, so the number of yellow went up and the number of spins went up.

Experimental probability is the ratio of the number of times an outcome does occur to the total number of trials or times the activity is performed.

When you did the spinner investigation, you also saw that after only one spin, neither experimental probability (the experimental probability of blue or the experimental probability of yellow) were close to 50%. After 10 spins, the experimental probabilities were closer to 50%. After 11011 spins, both the experimental probability of blue and the experimental probability of yellow were much closer to 50%.

Take a look at the following data:

The above data shows that, as we increase the size of our sample, the experimental probability gets closer and closer to the theoretical probability.