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Volume V
The Basketball
Tournament
By Patty Geroulis
Abstract: Through
the use of recurrence relations, we are able to find the probability that each
team makes it to the finals in an n-team tournament.
Hamming Codes
By Patty Huth and Abby Liss
Abstract:
Given an independent probability ‘p’ of error in each bit
of a transmission, we show that there is an advantage to transmitting a message
as a Hamming Code when p less than .5 per bit.
An Algorithm for
Weighing Marbles
By Mark N. Short
Abstract: We
wish to consider the problem of weighing marbles.
Assuming that we are given a set of marbles and that all marbles weight
the same except for one, we wish to develop a function that relates the number
of marbles we are given to the minimum number of weighings required to determine
the ‘bad’ marble and whether it is heavy or light.
To this end, a recurrence relationship was discovered through an
algorithm which let us determine the minimum number of weighings for any even
number of marbles up to 12.
Convex Hull
Problem on the Circle
By Tomislav Galac
Abstract:
We will derive the formula for computing the probability that the
convex hull of n randomly chosen points on a circle contains the center of the
circle. Though
continuous in its nature, this problem is solved by methods of discrete
probability that avoid the use of integration techniques.
Do We Have a
Winner?
By Diana DeFranco
Abstract:
We will use digraphs to determine the probability of producing a
Condorcet winner in the Condorcet voting method.
Balls in Bags
By Victor Griffin and David Albee
Abstract: In
the game Balls and Bags, pairs of balls are removed from a bag containing red
and black balls.
We give the probability of running out of red balls through a recurrence
relation.
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