GAINING A BETTER UNDERSTANDING OF FAILURE PROBABILITIES

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SOUTH PLAINFIELD, NJ - When a trial or event which occurs over a finite period of time, it is one of the most misunderstood facets of basic probability.  It is my hope that this column will do something to alleviate that misunderstanding.

PICK A NUMBER, ANY NUMBER

QUESTION #1:  I ask you to pick any number which is greater than equal to one and less than or equal to ten, or more concisely – one to ten inclusive by rolling a 10-sided die.  What is the probability that your number WILL NOT be picked?

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Since I will only be successful 10% of the time, I will be unsuccessful 90% of the time – which also can be expressed as 9/10 or 0.9.

QUESTION #2:  What is the probability that your number WILL NOT be selected if I roll the die ten times given the fact that the probability of being unsuccessful is 90%?

Because we are repeating the same trial with the same criteria, each trial is independent of one another, because when we do something such as roll a die, flip a coin, or spin a roulette wheel, or play a slot or video poker machine – any previous results do not have any impact on the present outcome or any future outcomes.  Many of you might have heard the saying “the dice have no memory.”  That is a superb non-numerical explanation which explains a numerically-based concept.

This time, our answer is a bit more complicated.  You just take 0.9 and multiply it ten times (0.9^10), giving you answer of 34.87% - a bit higher than most people might think it would be.

What about repeating this 20 times or 30 times?  The chances that your number will not come up when you repeat this 20 times, or two cycles is 12.16% - a little short of one out of every eight times.  For 30 repetitions or three cycles, the probability of your number not coming up is 1.48% - or about once every 68 times; improbable but certainly not impossible.

WHAT ABOUT EXAMPLES WITH MORE NUMBERS TO CHOOSE FROM?

It’s the same thing, even with numerical computations that are a bit more difficult.  A great example is that of a video poker machine.  The probability of success when hitting a royal flush for most standard video poker games is 1/40,000.  That means that the probability of NOT getting a royal flush in 40,000 hands is the number 0.999975 multiplied over and over 40,000 (0.999975^40,000) times – which amazing only reduces to probability of failure to 36.79%.

To keep things a bit more basic, we can just select any number between one and 40,000 inclusive.  If we keep going and multiply 0.999975 over and over 80,000 times – we get 13.52%. Put another way, if you picked a number between one and 40,000 inclusive, there’s more than a one in seven chance that your number WILL NOT be picked. 

Say you want to go to 120.000 or three cycles – there is 4.98% of that occurring, or a one in twenty chance that the number you select WILL NOT be picked.

QUESTION #3:  Does this relate to lottery?

ABSOLUTELY, but analyzing that is much more complicated than it appears since the numbers that people are not all picked randomly (they do all have an equally likely chance of occurring).  That will make a perfect article for another time.

 Greg Heim has been a lifelong, Central NJ resident, and a resident of South Plainfield for over 13 years.  Greg’s wife Lisa has almost 20 years of full-time experience as a high school science teacher, and has worked at South Plainfield High School since 2005.  Greg and Lisa’s daughters Rosalind, 17, and Stephanie (“Steffi”), 16, also attend SPHS.  Their 10-year-old son Michael (“Mikey”) has special needs as a high-functioning autistic student.  He attends Kennedy Elementary School where he has made tremendous progress.

Autism is something that Greg Heim knows a lot about.  Even though he was not diagnosed with Asperger’s Syndrome until the age of 40 in 2006, Greg and pretty much anyone who has ever met or corresponded with him, even remotely knew that he was very different. The “label” proved to be a positive, life-changing event not only for him, but for his family and close friends as well.

Providing discussions and presentations about Asperger’s is only one area that Greg offers our communities free of charge.  Greg is also a well-known and respected numismatic researcher with over 40 years of experience.  His interest in coin collecting began in second grade after carefully examining a large bag of Lincoln “Wheat Ear” Cents coined from 1909-1958.  In addition to his scholarly contributions in the numismatic community, Greg’s involvement in the governance of numismatic clubs on the local, state, and national levels began and has continued since his junior year of high school in 1982.  Greg’s numismatic presentations are applicable for those with or without numismatic experience.  His most popular programs geared towards non-numismatists come in the areas of selling a collection and avoiding fraud when purchasing precious metals for investment.

Greg received his Bachelor’s in mathematical sciences from then-Kean College in 1996.  Greg’s specialties lay in the areas of reinforcing the importance of basic, arithmetic operations, and out-of-the-box thinking that goes beyond standardized tests – especially when it comes to the mathematics and psychology related to games of chance.   Greg’s career as a professional poker and video poker player and author for more than a decade is something that he enjoys sharing with others, especially high school students as an educational primer. When Greg was asked why his passion to lecture on this subject was so high, he stated “because there is an incredulous lack of knowledge and misinformation about the reality of gambling to which race, gender, education level, income level, geography, and any other societal dynamic one can think of have little or zero influence. “

Greg is also an avid sports historian and enthusiast in the areas of football, basketball (college and professional), baseball, hockey, and boxing to a lesser extent.  Greg is a lifelong New York Yankee fan, and spent over eight years in the sports card and memorabilia business from 1986-1993, and he has been a stalwart fan of Nebraska Cornhuskers football since 1982.  His most popular sports programs come from zeal as a diehard, New Jersey Husker fan.

Greg’s approach to providing presentations usually relies on a cooperative effort with the person who has the most contact with his potential audience in order to optimize the number of people in said audience while providing them with the presentation that they most likely want to hear.

But sometimes it does not even have to be all that complicated.  Greg loves to be grilled and put on the spot for 60-90 minutes with a basic “Q&A” format, or one to which he just sits in a chair and plays the role of a raconteur.

For more information, please go to Greg’s community Facebook page “Gregory S. Heim.”  He can also be reached via e-mail at gynandroidhead@yahoo.com, or on his cell at 908-405-6408.

The opinions expressed herein are the writer's alone, and do not reflect the opinions of TAPinto.net or anyone who works for TAPinto.net. TAPinto.net is not responsible for the accuracy of any of the information supplied by the writer. 

The opinions expressed herein are the writer's alone, and do not reflect the opinions of TAPinto.net or anyone who works for TAPinto.net. TAPinto.net is not responsible for the accuracy of any of the information supplied by the writer.

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