
Let's clarify some vocabulary associated with probability.
These terms can be a bit confusing, so please read carefully.
Part I: 

Probability is how likely something is to happen. It is expressed using numbers between 0 and 1. 
Examples: 
• The probability of flipping heads on a coin is 1/2.
• The probability of tossing a 3 on a die is 1/6. 


An outcome is a possible result from an experiment. 
Examples: 
• The number 3 is a possible outcome of rolling a die.
• Getting a "tail" is a possible outcome of tossing a penny.
• The 2 of hearts is a possible outcome from choosing a card from a deck. 


A favorable outcome is an outcome that satisfies the conditions of an event (the result we are looking for, the outcome of interest). 
Examples: 
• Count number of times a 3 is rolled on a die (3 = favorable outcome),
• Winning if a heads on tossed coin (heads = favorable outcome).
• Record spinning an even number (even numbers = favorable outcomes). 


An event is a collection (subset) of the outcomes from the set of all possible outcomes. It is one or more of the possible outcomes. 
Examples: 
• An event could be the rolling of a 5 with a die.
• An event could be the rolling of a number less than 4 with a die.
• An event could be the tossing of a head on a penny and rolling a 3 on
a die. 


A simple event (or single event) is an event with a single outcome. 
Examples: 
• Probability of rolling a 4 on a die.
• Probability of flipping a coin and getting heads.
• Probability of getting a number less than 4 when rolling a die.
• Probability of drawing the ace of hearts from a deck of cards. 


An experiment is any procedure that can be repeated and has a defined result.

Examples: 
• Experiments: rolling a die, tossing a coin, picking a card from a deck, tossing a coin and spinning a spinner, tossing a coin three times in a row. 


Don't confuse "experiment" with "event"!
We think of "events" as big happenings, like the hiphop concert event at the dome. But in probability, the term "event" is less grandiose. The big encompassing word in probability is "experiment". The word "event" is just one act in the experiment.
The "event" is not rolling a die. The "experiment" is rolling a die. The "event" is rolling a 5 on the die. 

A trial is a repetition of an experiment.

Examples: 
• A die is rolled 20 times and each result recorded. Each individual roll
is called a trial within the experiment of all 20 rolls. 


Equally likely to occur means each outcome occurs with equal probability. 
Examples: 
• Rolling a 3 on a die and rolling a 5 on a die are equally likely to occur
(both have a probability of 1/6).
• Tossing a heads on a penny or a tails on a penny are equally likely to
occur (both have a probability of 1/2). 


Experimental probability, or relative frequency, or empirical probability relates to the outcomes of an experiment. It is calculated from the number of times an event occurs in the experiment, divided by the total number of trials in that experiment. 



Theoretical probability is the "expected" probability based upon knowledge of the situation. It is the number of favorable outcomes to the total number possible outcomes. 



A uniform probability model is one where the probabilities of the outcomes are equally likely to occur. 
Examples: 
• Probability of rolling a 4 on a die has only one outcome.
• Probability of flipping a coin and getting heads has only one outcome.
• NOT an uniform probability model: Probability of choosing a red card
from a deck of playing cards, has 26 possible outcomes  26 red cards.


Part 2: 
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A sample space is the set of all possible outcomes. 
Examples: 
• When rolling a die, the sample space is the set {1, 2, 3, 4, 5, 6}. 


A tree diagram is a diagram that has branches that show all of the possible outcomes of an event. Particularly helpful with compound events. 
Examples: 
• Drawing branches to show the probability of flipping a coin followed by rolling a die. 


A compound event is a combination (union) of two or more simple events happening together (with two or more outcomes). 
Examples: 
• Probability of rolling an even number on a die, then tossing a head on
a penny.
• Probability of tossing three pennies and getting at least 2 heads.
• Probability of drawing a heart from a deck of cards, replacing the card,
then drawing a spade.
• Probability of drawing a red ace from a deck of cards, not replacing
the card, then drawing a black ace. 


Independent events are events that do not depend on each other. One event does not have an effect on another event. The outcome of one event does not affect the probability of the other event.

Examples: 
• Toss the same coin twice.
• Pick a marble from a bag of marbles, replace the marble, then pick
another marble. 


Dependent events are events that depend on each other, where one event has an effect on another event. The outcome of one event affects the probability of the other event.

Examples: 
• Draw a card from a deck of cards, then draw another card from the
deck without replacing the first card. 


Random describes outcomes that occur at random if each outcome is equally likely to occur. 
Examples: 
• Draw names from a hat.
• Use a random number table.
• Use a calculator to generate random numbers 


Simulation is a way of collecting probability data using objects such as coins. An experiment that models an actual event. 
Examples: 
• Using a penny and a 3section spinner to model choosing 1 of two outside doors in a building and then using 1 of 3 inside stair cases. 

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