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 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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: : Binomial distribution, standard deviation: Theory and software. 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 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%! The probability to get 5 “heads” in 5 tosses represents, actually, the probability of “5 heads in a row” (3.125%). Analysis of "FORMULA, software, gambling, binomial distribution, standard deviation, Super Formula.EXE at www.saliu.com. "FORMULA.EXE: software to perform sophisticated gambling and probability calculations: degree of certainty standard deviation binomial distribution. Calculate odds and binomial distribution probability. Get free software in mathematics, theory of probability, gambling formula. Statistics of drawings, coin, coin tossiing, standard deviation, 3 SD, 3 standard deviations for mean average. How to analyze drawings and the best method of numbers winning, combinations in random events related to normal probability rule. Rule of fluctuation, fairness, fair political vote and voting polls. Statistics of polling, election, elections. Presenting facts about players and gambling copyright. Standard Deviation, Variance, Variability, Fluctuation, Volatility, Variation, Median, Mean Average. The book of FORMULA, software, gambling, binomial distribution, standard deviation - and the special Super Formula.EXE. FORMULA.EXE and Super Formula (32 bit) can calculate fundamental formula of gambling, FFG, FTG, standard deviation, degree of certainty, number of trials. The best software to calculate binomial distribution formula, binomial standard deviation. Also calculator of odds, probability as exactly, odds as at least, probability as at least, odds as at most, probability as at most. Title: "FORMULA software upgrade: gambling, binomial distribution, standard deviation". The feature-rich FORMULA software was upgraded. The program covers gambling, probability calculations: standard deviation, binomial distribution, Gauss curve, normal distribution, odds, median.

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