Re: Risk/probability interactions with the public

[Bernard L Cohen <blc+@pitt.edu>]

On Wed, 29 Jul 1998, Dukelow, James S Jr wrote:

> 
> 
> On 29 July 1998 Bob Giansiracusa wrote:
> 
> > On the other hand, if one interprets the statement of the odds 
> > "really" being 1 in 80 million (for a $250,000,000 win), the expected 
> > return on the $1 investment is $ 250/80 = $3.125 -- also not a bad 
> > investment.
> >
> 
> Well, not quite.
> 
> A single Powerball ticket's probability of matching the six numbers is 
> 
>         p = 1.249E-8   or one chance in 80 million
> 
> You have to match 5 white balls numbered 1 through 49 and match the red 
> ball, chosen from red balls numbered 1 through 42. 
> 
> However, if there are 100 million tickets sold for this drawing, we can 
> use a binomial distribution with  N = 1.0E8 and p = 1.249E-8  or a 
> Poisson distribution with  lamda = N*p = 1.249  to calculate the 
> probabilities of 0, 1, 2, ... winners in the drawing.  If there are two 
> or more winners, then the $137 million immediate payout will be split 
> among the winners.  The $250 million dollars is the annuitized payout 
> of $10M per year for 25 years, so if you are calculating the expected 
> value of your $1 ticket, you should use either the immediate payout 
> (less taxes, of course) or the net present value of the annuitized 
> payout (less taxes, of course). 

	-I heard that $500 million in tickets were sold.
> 
> 
Bernard L. Cohen
Physics Dept.
University of Pittsburgh
Pittsburgh, PA 15260
Tel: (412)624-9245
Fax: (412)624-9163
e-mail: blc+@pitt.edu


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