Best AIME Problem
Here is a changed version of the best AIME problem ever.
The probability of rolling 10 heads and 14 tails(on an unfair die) is 1/81 times the probability of rolling 14 heads and 10 tails.Find is is the probability of rolling a heads.
The answer is 7.
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1 solution
Set up the equations (1-p)^14 p^10=1/81 ^p^14*(1-p)^10.Just divide off powers of 10,take the fourth root of both sides,and solve the remaining two step equation.p=3/4.3+4=7.