1980 Canadian MO Problems/Problem 4

Problem

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

Solution

See Also

1980 Canadian MO (Problems)
Preceded by
Problem 3
1 2 3 4 5 Followed by
Problem 5