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Applications of Probability

Examples of probability and statistics being used in everyday life.

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Are banking and weather forecasting the only careers that use statistics? If you plan to go into music or film production, or perhaps advertising, do you really have any use for statistics or probability?

Read on, in this lesson we will discuss careers that rely on statistics and probability – some may surprise you!

Careers Using Probability and Statistics 

Credit: Trausti Evans
Source: https://www.flickr.com/photos/114303073@N05/11934570484/
License: CC BY-NC 3.0

Professional musicians and music producers depend on knowing what types of music are most popular among members of their target audience. A great jazz song will probably not be a platinum-seller if marketed to middle and high school students, and the latest rap sensation is probably going to be much less popular among the over-50 demographic than among teens! Even the right kind of music for a particular audience may not be ideal to release at specific times of the year (think Christmas music in June), and otherwise less popular songs may be ‘hot’ due to other factors (when an 80’s song is used in a hit movie, sales of the original album can skyrocket).

Statistics can be remarkably helpful in determining when to record or produce a particular song or album based on how consumers have responded to similar situations in the past. Considering the number of people whose incomes depend on making the most of sales, it is no surprise that musicians and producers alike take the calculation of prime release dates and music types very seriously. For instance, if you release a Christmas song remake too soon, it’s old news by the time the actual holiday comes around and nobody wants to buy it as a present. Release the same album too late, and people may have already purchased all of the holiday gifts they can afford.

Naturally the situation is similar for film production and actors/actresses. A movie about the world trying to avoid a giant asteroid may be reasonably popular in any season, but if it is released during the summer (when the biggest movie-going crowds are out of school) and right after a big news report about a comet visible in the sky… now the same movie is a multimillion dollar blockbuster!

In fact the concept holds true for pretty much any product that is sold to a wide audience: the more accurately a statistician can evaluate the data for a particular product or market, the more successful the sales may be if those statistics are properly put to use.



Real-World Application: DJing

DJ Woodz, the popular artist, is hoping to release his next Platinum Record. He learns that a recent study suggests that songs about expensive streetcars are popular right now with 62% the 19-23 year-old male crowd. Woodz also stumbles across an article that hints that a big blockbuster movie about country music will be released soon. He knows from experience that songs about making it big as a rap singer have been rather consistently well received by about 45% of males ages 17-25.

Credit: three6ohchris
Source: https://www.flickr.com/photos/three6ohchris/2133491020
License: CC BY-NC 3.0

How might these statistics help him to plan out his next album?

E.Z. can certainly make good use of the first and last statistics by recording a few songs about singers making it big and driving expensive cars! He may want to try to time the release of his album before the big movie about country music comes out, or perhaps delay it until the excitement of the film dies down. By factoring in as many accurate statistics as appropriate, Woodz can make the most of his next album.

Real-World Application: Retail Clothing Stores 

Based on what you know about the application of statistics in the music and film business, can you identify some ways that statistics might benefit a retail-clothing store?

Successful clothes retailers continuously monitor statistics such as:

  • Styles and colors that sold the best at the same time in previous years
  • Popular trends in style, cut, and color in trend-setting areas
  • Current preferences based on specific demographics
  • Brands and styles currently popular at competing retailers

Real-World Application: Law Enforcement 

How might the application of statistics help a police officer, or an entire police force, make the most effective use of their limited funds to help keep people safe?

Police officers apply statistics in a number of ways. By monitoring which intersections have the most accidents, patrolmen can pay particular attention to ensuring that people drive carefully in those areas. By monitoring weather statistics, officers can be prepared for dangerous trends in the kinds of weather (snow, high winds, heavy rain), which may lead to greater need for men on duty.

Earlier Problem Revisited

Are banking and weather forecasting the only careers that use statistics? If you plan to go into music or film production, or perhaps advertising, do you really have any use for statistics or probability?

It is probably pretty clear now that there are many, many careers that rely on an understanding and application of probability and statistics.

Certainly weather forecasters and bankers monitoring interest rates use statistics daily, but so do sales managers and advertisers in nearly every market from food to clothes to entertainment. Without understanding the appropriate statistics, many (or all) of the biggest companies you know of would probably never have become successful in the first place.


Example 1

What use would a travel agent have for statistics?

Travel agents can be very helpful to travellers by knowing the statistically least expensive times to travel to a particular destination, or by knowing about location that are statistically more likely to be rated highly by a particular kind of traveller, among many other things.

Example 2

How might someone who has to prepare for hurricanes and tornadoes use statistics?

By studying the most active locales and seasons for dangerous weather, a person responsible for mitigating risk from such things can improve the chances that the potential victims have time to prepare.

Example 3

How might a stock broker use statistics?

Stock brokers monitor the statistically likely influencing factors for different kind of stocks, in order to make educated guesses about potential price increases and decreases. Because a good broker can more often predict when a price is about to increase, he or she is in a better position to buy the stock at a lower price and re-sell it shortly afterward for more money.


A June 2008 study by the U.S. Travel Association suggested that air travelers avoided an estimated 41 million trips over the previous 12 months because of frustration over the hassle of flying. The missed trips cost the U.S. economy more than $26 billion. Also, nearly 50 percent of travellers polled said that they believe the air travel system is not likely to improve in the near future. 

The extended effect of avoided trips was also costly to other industries; hotels lost almost $6 billion and restaurants more than $3 billion. Even federal, state and local governments lost more than $4 billion in tax revenue because of reduced spending by travelers. (Source: Air Travel Survey, 2008)

  1. How might a car salesman make good use of these statistics?
  2. Would this information be useful to a potential restaurant owner?
  3. How might a car-rental company make use of this information to boost rentals?
  4. Based on the number of lost trips, how much does the loss of a single trip, on average, cost the US economy?
  5. How might the government’s loss of tax revenue negatively affect the travellers who choose to stay home and perhaps take a less expensive driving vacation closer to home?

Business travel in the U.S. is responsible for $246 billion in spending and 2.3 million American jobs; $100 billion of this spending and 1 million American jobs are linked directly to meetings and events. For every dollar productively invested in business travel, businesses experience an average $12.50 in increased revenue and $3.80 in new profits. (Source: The Return on Investment of U.S. Business Travel)

  1. What kinds of business would benefit from learning these statistics?
  2. Do these numbers mean that every business should spend money on business travel?
  3. Would these statistics be of interest to hotel owners?

The Hispanic/Latino population in the U.S. is expected to reach 47.8 million by 2010, representing 16 percent of the total population. By 2050, the Hispanic/Latino population is projected to total 102.6 million, comprising 24 percent of the U.S. population. In 2007, there were an estimated 16.2 million Hispanic adult leisure travelers who took a combined 50.4 million domestic and outbound trips and spent $58.7 billion on their travels. (Source: Profile of Hispanic/Latino Leisure Travelers, 2008 Edition)

  1. How might these statistics be of use to a travel agent?
  2. Would these statistics benefit a restaurant owner?
  3. How could the owner of a bed and breakfast inn make use of these statistics?

Review (Answers)

To view the Review answers, open this PDF file and look for section 1.2. 

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Combinations are distinct arrangements of a specified number of objects without regard to order of selection from a specified set.


A consumer is anyone who purchases or uses a particular product or service.


If something is counterintuitive, it is not what you might initially guess.


Data is information that has been collected to represent real life situations, usually in number form.


A demographic is a specific group of consumers chosen by age, sex, religion, home country, place of residence, music preference, or any other specified characteristic.

fair die

A fair die is a die with an equal chance of landing on any side.

Fundamental Counting Principle

The Fundamental Counting Principle states that if an event can be chosen in p different ways and another independent event can be chosen in q different ways, the number of different arrangements of the events is p x q.


A permutation is an arrangement of objects where order is important.


When everyone or everything in a population has an equal chance of being selected, the selection can be said to occur at random.

sample point

A sample point is just one of the possible outcomes in a sample.

Target Audience

A target audience is a particular demographic that is intended to be the main group of consumers of a particular product or service.

unfair die

An unfair die would be more likely to land on a particular number than the others.


In statistics, a variable is simply a characteristic that is being studied.

Image Attributions

  1. [1]^ Credit: Trausti Evans; Source: https://www.flickr.com/photos/114303073@N05/11934570484/; License: CC BY-NC 3.0
  2. [2]^ Credit: three6ohchris; Source: https://www.flickr.com/photos/three6ohchris/2133491020; License: CC BY-NC 3.0

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