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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!

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.

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..

Probability Theory Practice Tests

Common Core: High School - Statistics and Probability Diagnostic Tests

Many students fall into the trap of assuming that the results of one trial influence the theoretical probability of future trials, but that's not true. For example, the theoretical odds of flipping heads on a fair coin are $\frac{1}{2}$ no matter how many times it's come up in a row. If the student in your life is having a hard time grasping this, an experienced math tutor could look for fresh explanations and examples to drive the point home. Contact Varsity Tutors today for more info.

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