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Make predictions

One of the most powerful abilities of probability is the ability to make predictions.  By knowing the probability of an event occurring, we can make a guess as to how many times the event will occur over time.

Out of the people who have already signed up for a genetics lecture, 6 people have blue eyes while 4 people do not. Considering this data, how many of the next 30 people to sign up should you expect to be blue-eyed?

First write the experimental probability as a fraction in simplest form.

$p(blue)=\frac{blue}{total}=\frac{blue}{blue+other}=\frac{6}{6+4}=\frac{6}{10}=\frac{3}{5$

The experimental probability is $\frac{3}{5}$

We can predict the outcome of the second set of trials by assuming that the ratio will be the same as in the first set of trials. Write a proportion by setting the two ratios equal to each other, then solve.

 $\frac{3}{5}=\frac{n}{30}$ 3×30 = 5n Find the cross products 90 = 5n Simplify 18 = n Divide both sides by 5

You should expect 18 of the next 30 people to be blue-eyed.