Sunday, March 25, 2007

Probability in the Real World

In doing my research, I have come to realize that probability is one of the most prominent uses of mathematics in our everyday lives. Knowing the probability of a certain event happening or not happening can be very important to us in the real world. The following are examples of situations that take place in our everyday lives that involve the use of probability:

Weather Forecasting
Suppose you have some outdoor plans made for a particular day and the weather report says that the chance of rain is 70%. Should you still go ahead with your plans or should you cancel them for another day? Where does this forecast comes from? Meteorologist are able to calculate the likelihood of what the weather may be on a particular day by looking back in a historical database and examining all the other days in the past that had the same weather characteristics and then determine that on 70% of those similar days it rained. The mathematical formula for probability can be used to demonstrate these findings. When looking for the chance it will rain, this will be the number of days in the database that it rained is divided by the total number of similar days. For example, if there is data for 100 days with similar weather conditions (the sample space), and on 70 of these days it rained (a favorable outcome), the probability of rain on the next similar day is 70/100 or 70%. Since a 50% probability means that an event is just as likely to happen as not to happen, a 70% chance means that it is more likely to rain than not. Therefore, perhaps it is best that you stay home and reschedule your plans for another day!

Batting Average
A batting average involves calculating the probability of a player hitting the ball. The sample space is the total number of time a player has had at bat and each hit is a favorable outcome. Therefore, in 10 at-bats a player gets 3 hits, his or her batting average is 3/10 or 30%. For baseball stats, all the percentages are multiplied by 10, so a 30% probability translates to a 300 batting average. So let's say your favorite baseball player is batting 300. This means that when he or she goes up to the plate, they only have a 30% chance of hitting the ball!

Winning the Lottery
Millions of people around the world spend their money on lottery tickets in hopes of winning the big jackpot and become millionaires. But do these people realize how low their chances of winning actually are? Determining the probability of winning the lottery will allow you to see what the likelihood of winning truly is. The following formula is used to figure out the probability of winning Lotto 6/49:

The number of winning lottery numbers
The total number of possible lottery numbers

The Canadian 6/49 Lottery has 6 numbers drawn from a total of 49 balls with the numbers 1 through 49 on them. You must use the formula for permutations and combinations to figure out the probability of getting all 6 numbers in the correct order. The answer would be that the number of ways of choosing 6 numbers from 49 is 49C6 = 13, 983, 816 . Therefore the probability of winning the lottery is 1/13983816 = 0.000 000 071 5 (3sf), which is about a 1 in 14 million chance! The website
Permutations and Combinations helps to explain this area of probability in more detail. I came across the following link that provides a sampling of the odds of some of the World's Great Lotteries. Have a look: The Lottery Site

The Futures Channel
While doing my research I found a website that contained a short five minute video that really helped to illustrate probability at work in a real life situation. The film is about a probability map that was constructed by a mathematician and used to locate a sunken U.S. ship with
the largest sunken gold treasure in U.S. history. It would be a great film to show in your classroom when teaching probability because it will help children realize that what they learn in math class and be applied and used in the real world. The following is the link to the film:
Movie Title: Undersea Treasure

The following are references used while creating this blog:



kunika saraswat said...

gives gud info but smthing more would have helped

CrookedNose2131 said...

FYI the video is behind a paywall.