Re: Setting up a probability problem

• To: mathgroup at smc.vnet.net
• Subject: [mg22195] Re: [mg22150] Setting up a probability problem
• From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
• Date: Thu, 17 Feb 2000 01:24:32 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```on 00.2.16 4:35 PM, Ron Lenk at Ron.Lenk at fairchildsemi.com wrote:

>
>
> I'm having trouble figuring out the mathematical formulation of this problem.
> I have n events, each of which has probability P (say 20%) of occurring at any
> given time. How large does n need to be in order to give me a confidence level
> c
> (say 90%) that I have m (say 5) events occurring simultaneously? Help in
> clarifying my thinking would be appreciated.
>
>
>
From your formulation it sounds as if  "n events, each of which has
probability P (say 20%) of occurring at any given time" is the same as
having n trials of a single event with probability 0.2 of occuring (and 0.8
of not occurring). If so then what you have is just the binomial
distribution BinomialDistribution[n,1/5] (from the
Statistics`DiscreteDistributions` package). (I am also assuming that you
mean a confidence level of 90% that you get at least 5 events occuring.)

So now you want to find the value of n such that
1 -CDF[BinomialDistribution[n, 0.2], 4] >= 0.90.
This can be done with :

In[26]:=

FixedPoint[If[1 - CDF[BinomialDistribution[#, 0.20], 4] >= 0.90, #, # + 1]
&, 1]

Out[26]=
38

--
Andrzej Kozlowski
Toyama International University
Toyama, Japan
http://sigma.tuins.ac.jp/

```

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