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# Probability

In mathematics, probability is a measure of how likely something is to happen. It is generally expressed as a number between 0 and 1, with 0 representing impossible events and 1 representing certain outcomes. In this article, we'll explore the basics of how probability works. Let's get started!

## How probability works

Let's say that you pick a random letter out of the following: J, K, L, M, N. All five letters are consonants, so the odds of choosing a consonant would be 1. Likewise, there are no vowels to choose so the odds of getting one would be 0. The odds of choosing K is $\frac{1}{5}$ , $20%$ , or 0.2.

Generally speaking, we can calculate probability using the following formula:

$P\left(\text{event}\right)=\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}}$

Notably, this formula is used for theoretical probability. If you actually choose a letter, flip a coin, or roll a die, you're working with experimental probability when you report your results. Experimental probability gets closer to theoretical probability the more trials you perform.

## Practice question on probability

a. What are the odds of rolling an odd number on a fair six-sided die that isn't a 3?

When we roll a six-sided die, we could get 1, 2, 3, 4, 5, or 6. Three of those are odd $\left\{1,3,5\right\}$ , but ones of those is a 3 so the number of favorable outcomes is 2. There are 6 possible outcomes. Using our probability formula, we get 2/6. We can express that as either $\frac{1}{3}$ , $33.33%$ , or 0.333..

## Flashcards covering the Probability

Statistics Flashcards

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