Problem:
A coin is altered so that the probability that it lands on heads is less than than and when the coin is flipped four times, the probability of an equal number of heads and tails is . What is the probability that the coin lands on heads?
Answer Choices:
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Solution:
Let be the requested probability. If the coin is flipped four times, the probability of heads and tails appearing twice is , and because it follows that . Solving for yields and because , the answer is .
The problems on this page are the property of the MAA's American Mathematics Competitions