Difference between revisions of "1980 Canadian MO Problems/Problem 4"

(See Also)
(Solution)
 
(One intermediate revision by the same user not shown)
(No difference)

Latest revision as of 07:25, 16 May 2024

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