```Date: Fri, 25 Feb 2005 05:06:14 -0500 Reply-To: ben.powell@CLA.CO.UK Sender: "SAS(r) Discussion" 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 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 ```

Back to: Top of message | Previous page | Main SAS-L page