MATHEMATICS  PROBLEM  #118
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Suppose that you draw numbers  x1 , x2 , x3 , ...  
randomly from the unit interval  [0, 1] 
using the uniform distribution* on  [0, 1] 
until the sum  x1 + x2 + x3 + . + xn  first exceeds  1.  
What is the probability that this happens on the fourth draw?  
That is, what is the probability that  x1 + x2 + x3  <=  1  
and  x1 + x2 + x3 + x4  > 1 ?

*With the uniform distribution on  [0, 1],  if  a  and  b  are any numbers
satisfying  0 < =a < =b < =1 ,  
then the probability that  a <= x <= b  is  b -a.
That is, the probability that  x  lies in any subinterval of  [0, 1]  is
the length of the subinterval.

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ADVANCED PROBLEM # 118.   
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In the above problem, what is the expected number
of draws until the sum first exceeds  1 ?

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Each midshipman submitting a correct solution to Problem 118 by noon on
Sunday 30 September 2001 will win a cookie, or  three cookies for
the advanced problem.  Submit solutions to Prof. Wardlaw
at mathprob@usna.edu (please no attachments!) or via his mailbox in
Chauvenet 301.

Correct solutions to Mathematics Problem #117 were submitted by Midshipmen
Alan Kruppa and Ralph Rogers.  Midn. Kruppa's solution is posted on the
board.  No one submitted a solution to Advanced Prob. 117.
My solutions to these problems are posted on the board on the Lab Deck
of Chauvenet Hall.