# Introduction to Probability

Statistically the most likely age group to have an auto accident is the 18-25 year old male group.

(They are young inexperienced drivers, and for some reason they don’t always seem to drive as carefully as other people do).

These young guys have the highest probability (or chance) of having an auto accident.

So a Car Insurance Company would be crazy to insure only 18-25 year old males as their Policy Holders.

Instead they need to “spread their risk”, and insure a range of drivers, including young people, as well as older people with good driving records.

Image Source: http://cdn.rsvlts.com

Likewise, an Insurance Company offering Fire Insurance would soon go broke, if they only insured people living in high “wild fire” danger areas in California, or dangerous “Bushfire” areas of Australia.

Such areas have a high probability or chance of fire damaging peoples properties.

Instead Insurance Companies need to have policy holders living in a variety of locations.

This way the premiums from the people living in areas where there are hardly ever fires, can cover the payouts for victims of high fire risk areas.

Insurance Companies use Probability, Statistics, and other advanced Mathematics to assess and cover risks. The experts who do this work are very highly paid people called “Actuaries”.

Introductory Videos on Probability

Watch these videos to learn about Probability.

This first video is a one minute Video about Probability being a value between 0 and 1.

This next video goes into more detail about Probability, and shows some examples of what the chances are of various things occurring.

The following video is a bit out there, but summarises most of the main concepts associated with Probability in less than ten minutes.

This video also covers combination proabilities which we will cover in a later lesson.

We apologize in advance if some people find the word “crap” offensive, or do not like some of the bizarre scenarios in this guy’s word problems.

Overall the Video is probably PG Rated.

The Video Word Problems are covered very quickly, and so you may need to pause and rewind the Video in some places.

Probability Summary

Here is a summary of the key points we need to know in relation to Probability.

Probability of 0% or 0 = cannot occur = impossible

eg. The sun rising in the West.

Probability of 100% = Definitely will happen

eg. Ice on your bare skin will feel cold.

The chance of any event happening is always in the range of 0% to 100%, or 0 to 1 if dealing in Fractions.

A 50% or 0.5 or 1/2 chance occurs for getting heads when you toss a two sided coin that only has a head on one side.

A 50% chance is not definite, and is only an approximation or estimate or average.

Eg. You could toss a coin 10 times and only get heads 3 times.

But if thousands of people all tossed a coin ten times, we would expect that the majority of them would get 5 heads and 5 tails.

There is a “Probability Scale” which looks like this:

Image Source: http://ictedusrv.cumbria.ac.uk

The Probability Formula for an even happening is as follows:

Pr(Event) = outcomes you want to get / total possible outcomes

If two independant events are involved, in an “AND” situation, then multiply the separate probabilities to get the answer.

Eg. For two coins tossed and there is heads on the first coin AND heads on the second coin:

Pr (HH) = P(HH) = 1/2 x 1/2 = 1/4

For one event “OR” the other one occurring, add the probabilities to get the answer.

Eg. Probability of Throwing a normal six sided dice and getting a 1 OR a 6 = 1/6 + 1/6 = 2/6 = 1/3

Introductory Notes and Examples on Probability

The following two web pages have some great introductory notes and examples about Probability:

http://www.mathsisfun.com/data/probability.html

and

http://www.mathgoodies.com/lessons/vol6/intro_probability.html

The Math Goodies page, even has interactive spinners, and dice rollers on it, that you can click and make events happen.

Dice Simulators

For a great simple free online dice roller, which allows the user to roll between 1 and 60 dice at a time, click the following link:

http://www.random.org/dice/

The following freee online app has several dice simulations; but the sound effects can be a little annoying.

Click the link below to use this simulator

http://www.curriculumbits.com/prodimages/details/maths/mat0005.html

This dice simulator allows you to adjust the number of sides on the dice for interesting investigations.

Click the link below to use this simulator

http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks1/maths/dice/

Coin Simulator

This simulator does coins and dice, and you can choose what you want to do, for example: two dice.

As you spin the coins it also keeps a tally of your results.

Click the link below to use this simulator

http://www.subtangent.com/maths/coindice.php

Another Two Coins Simulator, where you can pick various world currency coins to use, can be found here:

http://www.random.org/coins/

Interactive Spinner

The following interactive allows players to spin the colored spinner, and it tallies the results as we go, provided that we click on the Results Button at the bottom of the screen.

Click the link below to use this simulator

http://www.mathplayground.com/probability.html

Probability Worksheets

Here are some worksheets that can be done to practice Probability Skills.

There are two similar worksheets with answers at the following PDF link:

Virtual School Videos on Probability

The “Virtual School” YouTube channel has an excellent set of videos on Probability.

Here are the main videos, which are all well worth watching.

Listing Probabilities and Sample Spaces Video

Probability Multiplication Rule

Example 1 of Multiplication Rule

Example 2 of Multiplication Rule

Probability – Tree Diagrams

The following two videos show how to use Tree Diagrams to answer Probability Questions.

Tree Diagrams can be used when we have Independant Events – the first event does not effect the second event.

Examples include tossing a coin twice, rolling a dice several times, or picking lollies or candies from a bag several times.

Part 1 Video – 6 minutes

Part 2 Video – 5 minutes

In this second video we look at sampling without replacement.

Probability Games

Here are some fun online games to play and practice Probability.

Carnival Probability Game

In this game, students learn the practical application of the concept of probability by playing carnival games.

The object is to win as many tickets as possible.

Click the following link to go to this game:

http://mrnussbaum.com/probfair-play/

Colored Balls Machine Probability Game

Click the following link to play this game:

http://www.kidsmathgamesonline.com/numbers/probability.html

Higher or Lower Card Game

Click the following link to play this game:

http://www.subtangent.com/maths/higher-lower.php

Zoo Animals Probability Race Game

This game is a little bit out there, but is good fun once you get into it.

Click the following link to play this game:

http://www.bbc.co.uk/bitesize/ks2/maths/data/probability/play/

More Online Probability Activities

There are lots of Games, Interactive Lessons, and Test Yourself Online activities at Mrs MacIntosh’s webpage:

http://www.tvdsb.ca/webpages/cmacintosh/mathematics.cfm?subpage=193944

There are plenty more Online Games and Interactives at the the Johnnies webpage:

http://jmathpage.com/JIMSProbabilitypage.html

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