Raffle Tickets

Date: 08/20/97 at 07:39:49
From: mostyn
Subject: Probability

What is the best way to do this:

A man buys 5 tickets in a raffle in which 100 tickets are sold.  If
there are three prizes in the raffle, find the probability that the 
man:

   (a) wins exactly one prize;
   (b) wins at least one prize.

I figured it out using a tree diagram, and multiplying probabilities 
of the branches, but is there a better way?

Date: 08/26/97 at 13:31:25
From: Doctor Rob
Subject: Re: Probability

Let C(a,b) = a!/(b!*(a-b)!).

   (a) C(3,1)*C(97,4)/C(100,5)  is the probability of choosing 
       one out of the three winning tickets and choosing four 
       out of the 97 losing tickets as a favorable result of 
       choosing five out of the 100 tickets sold.

   (b) This probability is 1 - C(3,0)*C(97,5)/C(100,5), since 
       the last term is the probability of choosing zero out of 
       the three winning tickets and five out of the 97 losing 
       tickets.

-Doctor Rob,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/