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) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{favorable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{outcomes}}$
 Experimental Probability
Experimental probability is based on data collected from repeated trials or surveys.
P(event) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{favorable}\mathrm{outcomes}\mathrm{based}\mathrm{on}\mathrm{trial}\mathrm{or}\mathrm{survey}}{\mathrm{Total}\mathrm{outcomes}}$
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)
P(Spades) = $\frac{13}{52}\mathrm{which}\mathrm{is}\frac{1}{4}$
Cheat Sheet
 Probabilities are usually expressed in $\frac{a}{b}$ form.
 A probability of 0 means an event can't occur.
 A probability of 1 means the event is sure to occur.
 Even though the probability is usually expressed as a fraction, it can be expressed as a decimal or percent.
 Rishi Jethwa
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