# Using Probability to Make Decisions

Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

You can improve your decision-making ability by using probability! In this lesson, you will learn how to apply the rules of probability to make better decisions.

## Basic Rules of Probability

Suppose you flip a coin 100 times. How many times will it land on heads? Even before you try this, you can use probability to give you an estimate of the answer. Probability is defined as the likelihood that a particular event will happen. For the coin toss example, we know that there are only two possibilities, heads or tails, for each flip of the coin. To calculate the probability of the coin landing on heads, divide the number of outcomes in which the coin lands on heads by the total number of outcomes possible. In this case, there is only one way the coin can land on heads out of two possible outcomes (heads or tails).

Probability of landing on heads = 1/2

That means that if you flip the coin 100 times, you can expect that half of the time, or 50 times, it will land on heads. This doesn't mean that every time you flip 100 coins, exactly 50 will be heads! However, if you flipped 100 coins many, many times, the average number of heads would be 50.

Let's look at a slightly more complicated example. Suppose that you roll two dice, one red and one blue. What is the probability that the sum of the numbers on the dice will be less than or equal to five?

First, we need to determine all the possible outcomes you could have when you roll two dice, and the number of those that have a sum less than or equal to five.

You can see that when you roll two dice, there are 36 possible outcomes, and of those, 10 are less than or equal to five. So the probability that the sum will be less than or equal to five is given by:

P(x) = 10/36 = 5/18

Now, why don't you try it? Using the table above, find the probability that the sum of the two dice is exactly seven.

Did you get 1/6? Great, that's right!

Let's look at it again in more detail. Once again, there are 36 possible outcomes, and out of those 36 possible outcomes, in six cases, the sum is exactly seven. That means the probability of getting exactly seven is 6/36 or 1/6.

## Decision making - Should you play that game?

Now let's use what we know about probability to decide whether or not it is a good idea to play a certain dice game.

You can choose to play one of two dice games, and you can't decide which is best. In both games, you roll two dice, and you will gain or lose money based on the sum of the two dice. In the first game, you will win \$7 if you roll a seven, but you will lose \$1 if you roll any other number. If you play many times, are you likely to gain or lose money, and how much? Probability can help you answer this question!

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