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Basic Statistics & Probability

Basic Statistics & Probability

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
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?

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.

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

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?

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