# At a Glance - Predicting vs. Observing Probability

There are two ways to calculate probability - either by using math to predict, or by actually observing the event and keeping score.

**Theoretical probability** uses math to predict the outcomes. Just divide the favorable outcomes by the possible outcomes.

**Experimental probability** is based on observing a trial or experiment, counting the favorable outcomes, and dividing it by the total number of times the trial was performed.

Let's look at this example: we tossed a coin 36 times and recorded the outcomes:

H, T, H, H, T, T, H, T, T, T, T, T,

T, T, T, H, H, T, H, H, T, H, H, H,

H, T, H, H, T, H, H, T, H, H, T, H

Based on this experiment:

- Experimental probability of flipping Heads is or about and Tails is or about
- Theoretical probability of flipping Heads is and Tails is

#### Example 1

A die was rolled 50 times. These are the results: 6 5 4 5 4 1 3 4 2 6 2 6 1 6 6 4 2 4 5 5 1 1 1 5 3 a) What is the experimental probability of rolling each number? b) And how do these compare to the theoretical probabilities? |

#### Example 2

Rowan drew a marble from this bag, recorded the color (blue, green, or orange), then replaced it and drew again. She did this forty times. Here are the results: g g g b b g g o g b Make a chart comparing the experimental and theoretical probabilities of drawing each color. |

#### Exercise 1

One card was picked from a standard deck of cards and the suit was recorded in a bar graph, then it was placed back into the deck and the process was repeated 50 times. Here are the results:

Answer questions below based on this data.

#### Exercise 2

What is the theoretical probability of drawing each suit?

#### Exercise 3

Which suit has the largest experimental probability, and what is it?

#### Exercise 4

Which suit's experimental probability is farthest from the theoretical probability, and by how much?