1988 AHSME Problems/Problem 28
Problem
An unfair coin has probability of coming up heads on a single toss. Let be the probability that, in independent toss of this coin, heads come up exactly times. If , then
Solution
We have , so we need to solve . Now observe that when , the left-hand side evaluates to , which is less than ; when , it evaluates to , which is more than , and when , it evaluates to again. Thus, since is continuous, the Intermediate Value Theorem tells us there is a solution between and and another solution between and , meaning that there is not a unique value of , so the answer is .
See also
1988 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 27 |
Followed by Problem 29 | |
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