Predicting vs. Observing Probability at a Glance

There are two ways to calculate probability:

using math to predict
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

Examples
Exercises

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
3 3 1 5 3 6 1 4 1 4 2 3 3 1 2 6 6 4 3 6 6 5 4 2 2

a) What is the experimental probability of rolling each number?

b) And how do these compare to the theoretical probabilities?

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Example 2

bag of marbles

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
b b g o g b o g o o
b b g o g g b g b o
g b g o g o g g o o

Make a chart comparing the experimental and theoretical probabilities of drawing each color.

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Example 3

Jermain and Tremain both calculate the predicted probability of getting heads if they flip a coin 10 times. Then they each flip a coin 10 times. a. Will they get the same number when they calculate the predicted probability? b. When they actually flip the coin 10 times, will they get as many as the probability predicted, for sure, no matter what? c. When they actually flip the coin 10 times, will Jermain absolutely, positively get the same number of heads as the Tremain?
a. Since they’re using the same formula to find the predicted probability, they will get the same number: .
b. The number of heads they flip is all up to chance. They should flip about 5 heads out of their 10 flips, but there’s no promise, no absolute way of knowing. The answer is no, there is no guarantee that they’ll flip 5 heads.
c. Because what they actually flip is up to chance, there is also no guarantee that Jermain will flip the same number of heads and the same number of tails as Tremain. It’s just flippin’ up to chance.

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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:

Frequency of card pick