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Quiz of the Month (Jun 2001)
Hector C. Parr
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SOLUTION TO LAST MONTH'S QUIZ
1). a) 10 b) 15 c) 21 d) 28
2). a) 5 b) 15 c) 35 d) 70
3) a) 4 b) 8 c) 16 d) 31 e) 57
Notes
1). The number of lines equals the number of pairs of
points, or _{n}C_{2}, or n(n1)/2.
2). The number of intersections equals the number of
quadruplets of points, or _{n}C_{4}, or
n(n1)(n2)(n3)/24.
3). If the lines are drawn one at a time, a new area is
formed whenever (i) an intersection occurs or (ii) a
line is completed. Initially there is one area, so
total is 1 + _{n}C_{2} + _{n}C_{4}.

THIS MONTH'S QUIZ
In an election there were only three parties. The Constrictive
Party gained c% of the votes, The Grey Party gained g% and
the Socratic Party gained s%, so that c + g + s = 100 (for
example c = 37.61, g = 18.23, s = 44.16.). But before publication
the three percentages were rounded to the nearest whole number,
giving C%, G% and S% respectively (in the example 38, 18, 44).
1. Find the probability that c differs from C by more than 0.25.
2. Find the probability that when the combined percentage vote for
the Constrictive and Grey Parties is itself rounded to the
nearest whole number, the result is not equal to C + G.
3. Find the probability that C + G + S = 101.

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(c) Hector C. Parr (2001)
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