FORMULA, software, gambling, binomial distribution, standard deviation, Super Formula.EXE.

Upgrade to FORMULA.EXE: standard deviation, binomial distribution

By Ion Saliu, Binomially At-Large

FORMULA, software, gambling, binomial distribution, standard deviation, Formula.

Written by Ion Saliu on January 27, 2001.

• FORMULA.EXE has been upgraded to calculate also the “Binomial Distribution Formula”. This formula calculates the probability of exactly M successes in N trials, when the probability p is constant. It deals with a sequence of events, such as a number of coin tosses. It proves that what happened in the past is relevant to the next trial. For example, we want to determine the probability of getting exactly 5 “heads’ in 10 tosses. We tossed the coin 7 times and recorded 5 “heads”. We toss the coin for the 8th time and get another “heads” (the 6th). We must stop the tossing; the experiment failed. We can no longer get EXACTLY 5 “heads” in 10 tosses. It is obvious that the previous events influenced the coin toss number 9.

A sequence of events means that the events do not take place at the same time. They occur one after another.
The “Binomial Distribution Formula” shows some interesting facts. For example, the probability to toss EXACTLY 1 “heads” in 10 tosses is only 0.98%. It is quite difficult to get only 1 “heads” and 9 “tails” in 10 tosses.
The probability to toss EXACTLY 5 “heads” in 10 tosses is 24.6%. It is not that usual to get exactly 5 “heads” in 10 trials, even if the individual chance of “heads” is 50%! We might have thought that we would get quite often 5 “heads” and 5 “tails” in 10 coin tosses. NOT! The chance is even slimmer to get 500 “heads” and 500 “tails” in 1000 tosses: 2.52%.
The probability to get 5 “heads” in 5 tosses represents, actually, the probability of “5 heads in a row” (3.125%).

The program handles now a wide range of potential user’s errors. I think it attempts to be “idiot-proof”…

There is a data type limit. The number of trials N must not be larger than 1500! There will be an overflow if you use very large numbers...


Ion Saliu

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