Date:         Fri, 25 Feb 2005 05:06:14 -0500
Reply-To:     ben.powell@CLA.CO.UK
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         ben.powell@CLA.CO.UK
Subject:      Re: Homework Exercise /Finance/Probability

Thanks, I'll have a look at this when I get a chance (pun?)

Ben.

On Mon, 21 Feb 2005 14:30:27 -0800, David L. Cassell
<cassell.david@EPAMAIL.EPA.GOV> wrote:

>ben.powell@CLA.CO.UK replied:
>> Worth a try :-) I bow to your superior knowledge. My probability is
>rusty!
>
>My knowledge isn't superior, just my attitude.  :-)
>
>> Ok, the probability all companies fail is 1*0.6^11 = 0.003628,
>resulting in
>> a loss of 12/11*11 = 12, plus the 5 in reserve gives a total pot of
>-7.
>
>No, if all 11 companies fail (at p = .6^11 as you stated), the result
>is 5 (million).  You lose everything invested, but no more.
>
>> The probability all companies win is 1*0.4^11 = 4.1943E-05, resulting
>in a
>> win of 12/11*11*10 = 120, plus the 5 in reserve gives a total pot of
>125.
>
>Yep.
>
>> How can there be a 60% chance of having a pot of at least 60 (or
>55+5)? A
>> pot of 65 can be achieved with 6 wins and 5 losses, not less, but
>there are
>> (?) only 462 chances of this combination of events occuring, out of
>2048
>> total. Add the probabilities of all the other better winning
>combinations (7
>> wins, 8 wins) and the probability of these winning scenarios is a
>quarter.
>> Where have I gone wrong?
>
>6 wins and 5 losses, each working with 1.090909 million, yields
>65.454545 million
>plus the protected 5 million, which is 70.454545 million.  5 wins and 6
>losses,
>each working with the same 1.090909 million, yields 54.545454 million
>plus
>5 million = 59.545454 million.
>
>Then you have to remember:  not all your combinations are equally
>likely, since
>p^k*q^(n-k) changes as k changes.
>
>To get to the 'bonus' result, you have to also consider the amount of
>money
>placed in reserve as a variable.  Put more money in reserve, and your
>maximum
>result goes down.. but the odds of going bust decrease.
>
>David
>--
>David Cassell, CSC
>Cassell.David@epa.gov
>Senior computing specialist
>mathematical statistician