2015 AMC 12B Problems/Problem 17
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 |
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