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

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== Problem ==
 
== 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. Prove that the probability of the student scoring [i]exactly[/i] <math>n</math> points is <math>\boxed{\frac{1}{3}\cdot\left(2+\left(-\frac{1}{2}\right)^{n}\right)}</math>.
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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. Prove that the probability of the student scoring exactly <math>n</math> points is <math>\boxed{\frac{1}{3}\cdot\left(2+\left(-\frac{1}{2}\right)^{n}\right)}</math>.
  
 
== Solution ==
 
== Solution ==

Revision as of 11:26, 2 March 2020

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
First Question
1 2 3 4 5 Followed by
Problem 3