Difference between revisions of "2015 AMC 12B Problems/Problem 17"
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Revision as of 18:00, 17 January 2016
Problem
An unfair coin lands on heads with a probability of . When tossed times, the probability of exactly two heads is the same as the probability of exactly three heads. What is the value of ?
Solution
When tossed times, the probability of getting exactly 2 heads and the rest tails is
Similarly, the probability of getting exactly 3 heads is
Now set the two probabilities equal to each other and solve for :
Note: also works, but it is assumed in the above that the problem writers meant where .
See Also
2015 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 16 |
Followed by Problem 18 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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