MathDB

3

Part of 2009 AIME Problems

Problems(2)

Weighted Coin

Source: AIME 2009I Problem 3

3/18/2009
A coin that comes up heads with probability p>0 p > 0 and tails with probability 1\minus{}p > 0 independently on each flip is flipped eight times. Suppose the probability of three heads and five tails is equal to 125 \frac{1}{25} of the probability of five heads and three tails. Let p \equal{} \frac{m}{n}, where m m and n n are relatively prime positive integers. Find m\plus{}n.
probabilityMATHCOUNTSnumber theoryrelatively primeAMC
Perpendicular Segments

Source: AIME 2009II Problem 3

4/2/2009
In rectangle ABCD ABCD, AB\equal{}100. Let E E be the midpoint of AD‾ \overline{AD}. Given that line AC AC and line BE BE are perpendicular, find the greatest integer less than AD AD.
geometryrectangleanalytic geometrygraphing linesslopefloor functionPythagorean Theorem