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 | + | 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 == | ||
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*[[1980 Canadian MO]] | *[[1980 Canadian MO]] | ||
| − | {{CanadaMO box|year=1980|before= | + | {{CanadaMO box|year=1980|before=Problem 3|num-a=5}} |
Latest revision as of 06:25, 16 May 2024
Problem
A gambling student tosses a fair coin. She gains 
point for each head that turns up, and gains 
points for each tail that turns up. Prove that the probability of the student scoring exactly 
points is 
.
Solution
See Also
| 1980 Canadian MO (Problems) | ||
| Preceded by Problem 3 |
1 • 2 • 3 • 4 • 5 | Followed by Problem 5 |
