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Gambling student tosses a coin, scores points

Source: Canadian Mathematical Olympiad - 1980 - Problem 4.

May 16, 2011
probabilityalgebrapolynomialcombinatorics unsolvedcombinatorics

Problem Statement

A gambling student tosses a fair coin. She gains 11 point for each head that turns up, and gains 22 points for each tail that turns up. Prove that the probability of the student scoring exactly nn points is 13⋅(2+(−12)n)\frac{1}{3}\cdot\left(2+\left(-\frac{1}{2}\right)^{n}\right).
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