1980 Canadian MO Problems/Problem 4

Revision as of 11:26, 2 March 2020 by Ellentilburg (talk | contribs) (Created page with "== Problem == A gambling student tosses a fair coin. She gains <math>1</math> point for each head that turns up, and gains <math>2</math> points for each tail that turns up....")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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 [i]exactly[/i] $n$ 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
First Question
1 2 3 4 5 Followed by
Problem 3