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 == |
Revision as of 11:26, 2 March 2020
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 First Question |
1 • 2 • 3 • 4 • 5 | Followed by Problem 3 |