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## Overview

If you are rolling a die and want to see your chances of getting a 6, probability can help!

## Probability

• A probability is the likelihood of a favorable or specific outcome happening.
• A probability of an event or Outcome always ranges from 0 to 1. The closer it is to 1, the more likely that event will occur.
• Here are a few terms to keep in mind:
• Sample Space or Total Outcomes: All possible results of an experiment are outcomes. If you are rolling a die, the total outcomes are 6. The sample space, in this case, is 6.
• Favorable Outcome (s): If you are looking for an even number, the total favorable outcomes are 3.
• Event: An event is a set of some favorable or all outcomes.

## Categories of Probability

There are two categories of probability.

• Theoretical Probability

Theoretical or actual probability where all outcomes are equally likely is:

P(event) =

• Experimental Probability

Experimental probability is based on data collected from repeated trials or surveys.

P(event) =

## Solved Examples

1. What is the probability of getting 6 when you roll a die?

Total outcomes: 6

Favorable outcome(s): 1

P(Getting 6) = $\frac{1}{6}$

2. You randomly pick a card from a deck of cards. What is the probability that it is of spade suite?

Total outcomes: 52 (52 cards in a deck)

Favorable outcome(s): 13 (13 spade cards)

• Probabilities are usually expressed in $\frac{a}{b}$ form.