# Probability

18.01.2019

Episode #9 of the course Everyday math by Jenn Schilling

Welcome to a quick dive into probability! Probability is a complex field of mathematics, but an introduction to it will help you better understand chance events such as weather, games of chance, sports, and more!

The Math

Probability tells us the likelihood of an event occurring. For example, a 60% chance of rain means there is a 60% likelihood that it will rain. There are a few important terms to understand around probability. The first is outcome, which is the result of an experiment or event. For example, in a coin flip, an outcome might be heads. The second is favorable outcome, which is the result that we are looking for. So, in a coin flip, perhaps we want to get tails; tails is the favorable outcome. The third is sample space, which encompasses the total possible outcomes of an experiment. For example, when flipping a coin, you can either get heads or tails, so the sample space consists of two outcomes: heads and tails.

To determine the probability of an event, we divide the number of favorable outcomes by the number of total outcomes in the sample space. For example, the probability of rolling a 3 on a six-sided die is 1/6 because there are 6 possible outcomes, but only 1 outcome in which we get a 3. In more complicated experiments, there are multiple ways of obtaining the favorable outcome.

For instance, suppose we are going to roll two dice, and we want to know the probability of getting a sum of 5. There are multiple ways of getting a sum of 5 from two dice:

1 + 4

4 + 1

2 + 3

3 + 2

We have a total of 4 favorable outcomes. There are 36 total possible outcomes for this experiment because each die has six sides that are all equally likely to occur (assuming we are being fair and not using weighted dice). So, the probability of rolling a sum of 5 is 4 (the number of favorable outcomes) divided by 36 (the number of total possible outcomes), which is 4/36, or 1/9 if we simplify. So, the probability of rolling a sum of 5 is 1 in 9.

Probabilities can also be turned into percents by dividing out the fraction. In our example above, the probability (or chance) of rolling a sum of 5 is 11%. The higher the percent, the greater the probability, and the more likely it is that the desired event will occur.

Everyday Applications

Probability appears frequently in our everyday lives. Whether it’s the weather forecast for the day, the lottery, or sports, probability is everywhere!

In weather forecasting, probability is used to indicate the chance of precipitation. This probability is calculated by using a sample space of all days with similar weather characteristics and evaluating the number of those days on which there was precipitation. For example, if the chance of rain is 60%, that means that out of all the days with similar weather conditions, it rained on 60% of them.

Games of chance and the lottery are another area in which probability is prevalent. In any game that involves dice, coin flips, cards, or spinners, the probability of a favorable outcome can be calculated as above in the dice sum example. Understanding the probabilities of certain cards or rolls can help anyone make better choices in games of chance.

In sports, probabilities appear in the likelihood of certain outcomes (who will win the game?), as well as in individual player statistics (how likely is it a certain player will hit the ball or make a field goal?). Knowing that the probability represents the likelihood of an outcome happening, based on all past events and whether the desired outcome occurred, helps us interpret and evaluate probabilities in various fields.

I hope you enjoyed this overview of probability. In tomorrow’s lesson, we will wrap up this course with an explanation of statistics! We will cover important statistical terms, and you will learn how to interpret statistics in sports, popular science, and the news.

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