This Applet, on the surface is very simple. It calculates your odds of getting N heads in a row tossing a coin. It also works when the coin is weighted. The same math also applies to anything you repeat over and over with the same odds. For example, what are you odds of escaping nuclear war for 80 years given the odds of escaping it one year. What are your odds of avoiding an earthquake for 90 years given the odds of having an earthquake in a given year. Using the probability enformation in the HIV Safe Sex tables, It can compute your odds of getting AIDS (Acquired ImmunoDeficiency Syndrome) given what you do and how often you do it.
Mankind does a number of things that amount to what the people in this mythical kingdom do. Every year the people gather and toss a large golden coin. The coin is heavily weighed to come up heads. If it comes up heads all is well for yet another year. However, if it ever comes up tails, the people explode all their nuclear weapons, release all their biotoxins and nerve gases, and their secret weapons and kill everyone. You can use the Applet below to see roughtly how long this civilisation lasts given how weighted the coin is.
Mathematician talk of probabilities rather than odds. If a coin every single time came up heads without fail because it was designed to, we would say it came up heads with probablity 1. If it came up tails every single time, we would call that probability 0. If it came up heads helf the time (a true coin), we would call that propability .5. If the coin came up heads ¾, then we would call than probability .75. Let’s say you entered .75 in the box labelled probability then entered 50 which means you are interested in the odds of getting 50 heads. The Applet will calculate a graph, showing you the odds of getting heads once, twice … all the way up to 50 times. You see the plunging toward 0 as the number of trials increases. It is realitively easy to get short strings of heads with a weighted coin, but even with that advantage, the effect of even one failing toss ruins the odds.
Let’s do a nuclear power accident. Throwing heads means running the plant for a whole year without it melting down. The odds are pretty good of doing this. You can estimate them by counting the number of nuclear plants, the total number of plantyears they have operated, and the total number of meltdowns. To do the calculation for a single plant, compute the odds of a good year as (1  probability of plant having an accident in a given year). Put that in the probability slot in the Applet. Then pick a number of trials, say 90 years (the projected lifespan of some child you care about). You can handle an accident or terrorist attack that detonates nukes, releases biowarfare, releases chemical weapons, a really nasty industrial accident, earthquake similarly.
The formula this program uses r = p^{t} only applies when the trials are independent, i.e. knowing the outcome of one trial does not give you a way to predict the next. For example, you could not use it on cicada populations since they have a regular seventeen year pattern. You could not use it for earthquakes which have a rough cycle and aftershocks.
Package  Version  Released  Licence  Language  Notes  

GoldenCoin 
1.0  20110612  free  Java 
❘ precis
❘ screenshot
❘ browse source repository
for the current version of GoldenCoin. Computes probability including odds or thrown heads N times in a row.
555K
zip for GoldenCoin Java source, compiled class files, jar and documentation to run on your own machine either as an application or an Applet.
Runs on any OS that supports Java e.g. W2K XP W2003 Vista W2008 W732 W764 W832 W864 W2012 Linux LinuxARM LinuxX86 LinuxX64 Ubuntu Solaris SolarisSPARC SolarisSPARC64 SolarisX86 SolarisX64 OSX. First install the most recent Java. To install, extract the zip download with WinZip, (or similar unzip utility) into any directory you please, often J:\ — ticking off the use folder names option. To check out the corresponding source from the Subversion repository, use the TortoiseSVN repobrowser to After you have installed the jar, you can run it as an application. Type: java jar J:\com\mindprod\goldencoin\goldencoin.jar
adjusting as necessary to account for where the jar file is. download ASP PAD XML program description for the current version of GoldenCoin. GoldenCoin is free. Full source included. You may even include the source code, modified or unmodified in free/commercial open source/proprietary programs that you write and distribute. Nonmilitary use only. 

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