## What is Probability?

Probability is a measure of how likely something is to happen. It is a measure of chance that best predicts what the outcome of an event will be. For example, when you flip a coin, it can land on either Heads or Tails. Before flipping, we have no idea what it will land on. We cannot predict the exact outcome, but we can analyze how likely an outcome is. The probability that the coin will land on Heads is ½, since it lands on Heads around half the number of times you flip it.

Here is the general formula for calculating the probability an event will happen: Ex. 1: There are three balls inside of a bag. Two of them are red, and one is blue. If I selected a ball from the bag at random, what is the probability that I pick a red ball?

1. The event we are interested in finding the probability of is picking a red ball.

2. The number of ways it can happen is 2: I pick red ball #1 or red ball #2.

3. The total number of outcomes is 3: I can pick the first red ball, the second red ball, or the blue ball. Using the above formula, we can calculate that the probability of picking a red ball is 2/3. If you were to repeat this experiment 300 times, you can expect the number of times you pick a red ball to be around 200, since 200/300 is the same fraction of probability as our answer, 2/3.

Ex. 2: What is the probability of rolling an even number on a die?

1. The event we are interested in finding the probability of is rolling an even number.

2. The number of ways it can happen is 3: I can roll a 2, 4, or a 6.

3. The total number of outcomes is 6: There are six numbered sides on a die, each with an equal likelihood of being rolled. Using the formula, we can calculate that the probability of rolling an even number is 3/6, or 1/2. If you were to repeat this experiment 300 times, you can expect the number of times you pick a red ball to be around 200, since 200/300 is the same fraction of probability as our answer.

## Likelihood

Because probability is always a fraction of the number of outcomes of an event, probability is always between 0 and 1. We can describe the likelihood an event will occur based on how large or small the probability is. ### If the probability of something happening is...

• Exactly zero, we say that the event is impossible. For example, the probability of picking a green ball from a bag of only red balls is impossible, because there are no outcomes in which you can pick a green ball.

• Greater than 0, but less than 1/2 (or 0.5), we say that it is unlikely to happen. For example, it is unlikely to roll a 1 on a die your first try (probability is 1/6), but it is still possible.

• Exactly 1/2 (or 0.5), we say that the event has an even chance of occuring; it is neither unlikely or likely. Flipping a coin is a good example of an even-chance event.

• Greater than 1/2 (or 0.5), but less than 1, we say that it is likely to occur. For example, it is likely to NOT roll a 1 on a die your first try (probability is 5/6 because you can roll 5 sides other than 1), but sometimes you will roll a 1.

• Exactly 1, we say that the event is certain to occur. For example, it is certain that you will pick a red ball if you drew from a bag with only red balls in it.