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Introduction to Probability

Learn what probability is and what are the uses of probability.
by

Kyle Laker

on 2 March 2015

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Transcript of Introduction to Probability

Introduction to Probability
What is probability?
A probability is a numerical measure of the likelihood of the event. It is a number that we attach to an event, say the event that we'll get over an inch of rain tomorrow, which reflects the likelihood that we will get this much rain.

A probability is a number from 0 to 1. If we assign a probability of 0 to an event, this indicates that this event never will occur. A probability of 1 attached to a particular event indicates that this event always will occur. What if we assign a probability of .5? This means that it is just as likely for the event to occur as for the event to not occur.
To find a basic probability with all outcomes equally likely, we use a fraction:

number of favorable outcomes
---------------------------------------
total number of possible outcomes

* What's a favorable outcome? It is the outcomes that fulfill the requirements of the question. For example, the number of outcomes on a spinner that are blue.

* What's the total number of possible outcomes? The total number of possible outcomes forms a set called a sample space.
Formula: How to Find Probability
Sample Space
The sample space is a set consisting of all the possible outcomes of an event (like drawing a marble from a jar, or picking a card from a deck). The number of different ways you can choose something from the sample space is the total number of possible outcomes.

Because each probability is a fraction of the sample space, the sum of the probabilities of all the possible outcomes equals one. The probability of the occurrence of an event is always one minus the probability that it doesn't occur.
Examples of Probability
Think for a minute about where you may have heard the words probability, chance, or odds? How is probability used in weather?
Chance of Rain
Odds of winning the Super Bowl
Chance of rolling a 3 on a dice
Odds of drawing a king from a deck of cards
Odds of picking a number from 1 - 10
Coin flip in sporting events
An experiment is a situation involving chance or probability that leads to results called outcomes.

An outcome is the result of a single trial of an experiment.

An event is one or more outcomes of an experiment.

Probability is the measure of how likely an event is.
Definitions
Problems
Experiment 1: A spinner has 4 equal sectors colored
yellow, blue, green and red. After
spinning the spinner, what is the
probability of landing on each color?




Outcomes: The possible outcomes of this experiment
are yellow, blue, green, and red.

Probabilities:

P(yellow) = # of ways to land on yellow = 1
total # of colors 4

P(blue) = # of ways to land on blue = 1
total # of colors 4

P(green) = # of ways to land on green = 1
total # of colors 4

P(red) = # of ways to land on red = 1
total # of colors 4
Experimental vs. Theoretical Probability
Experimental - The experimental probability of an event is the ratio of the number of times the event occurs to the total number of trials.

Theoretical - The theoretical probability of an event is the fraction of times we expect an event to occur if we repeat the same experiment over and over.
1. Toss a fair coin and observe the uppermost side. Since we expect that heads is as likely to come up as tails, we conclude that the theoretical probability is

P(H) = 1/2, P(T) = 1/2.

2. Roll a fair die. Since we expect to roll a "1" one sixth of the time,

P(1) = 1/6.
Experiment 2: A glass jar contains 6
red, 5 green, 8 blue and
3 yellow marbles. If a
single marble is chosen
at random from the jar,
what is the probability
of choosing a red
marble? a green marble?
a blue marble? a yellow
marble?

Outcomes: The possible outcomes of this
experiment are red, green,
blue and yellow.

Probabilities:

P(red) = # of ways to choose red = 6
total # of marbles 22

P(green) = # of ways to choose green = 5
total # of marbles 22

P(blue) = # of ways to choose blue = 8
total # of marbles 22

P(yellow) = # of ways to choose yellow = 3
total # of marbles 22
Probability Games
During this unit, we will playing several games that will introduce probability and allow us to have fun at the same time.
SKUNK
SKUNK is a game that allows students to learn the difference between choice and chance. The teacher rolls a pair of dice in front of the classroom. The dice are added up and every student receives that many points. After each roll, students must decide if they want to sit down for the round or continue standing. Once a student sits down, they are done for that round. If a student is still standing, the teacher continues to roll the dice until a 1 is rolled. Any student standing when a "1" appears on the dice will lose all their points for that round and they will put a 0 in their points column. There are 5 round in the game, S-K-U-N-K. The winner is the person who receives the most point after adding up the five rounds.
Probability Battleship
Probability battleship is a fun probability game that is played with a partner. Each player will place 5 markers on a number line from 1-12. The two players alternate rolling a pair of dice. The players will add up the dice and if the opponent has a marker on that number, they will remove it. A winner is determined when one of the players' markers are all removed.
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