What Is the Probability?

• The chance that something will happen is called probability.

• For example, if you toss a penny, what is the probability that it will come up heads?

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What Is the Probability?

• Most people would say “half and half,” and they would be right.

• The chance of a tossed penny coming up heads is 1⁄2, which can also be expressed as 0.5 or 50%.

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What Is the Probability?

• Probability is usually expressed as a number between 0 and 1 and written as a decimal rather than as a fraction.

• Suppose the penny comes up heads 7 out of 10 times. Does this result prove that the probability of a penny coming up heads is 0.7? No, it does not.

• What is the problem?

What Is the Probability?

• The problem is that the sample size—the number of objects or events sampled—is too small to yield an accurate result.

• In statistics, a sample is the group of individuals or events selected to represent the population.

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What Is the Probability?

• If you toss a penny 10 times, your sample size is 10.

• If you continue tossing 1,000 times, you are almost certain to get about 50% heads and 50% tails.

• In this example, the sample is the number of coin tosses you make.

• Scientists try to make sure that the samples they take are large enough to give an accurate estimate for the whole population.

What Is the Deviation?• Deviation tells you:

How close was what you observed to what was predicted/expected by probability.

– Probability will be a number between 0 and 1.– A deviation of 0 means you saw exactly what was

predicted by probability.– A deviation of 1 means you saw the complete

opposite of what was predicted by probability.– So, the close to zero, the closer what you

observed is to what you expected by probability

Sample Size vs. Deviation

• You will recall that increasing sample size decreases random errors, luck, coincidences, etc..

• Another way of saying this is “the more times you do something, the closer you should be to what is predicted by probability.

• Therefore, increasing sample size should decrease deviation.

• Be careful, sometimes in life you don’t always see what you expect.