Function - sequence question and a clever probability that requires close attention to the framing of the problem.

Difficulty: Medium, if only because the function makes the pattern elusive. Once you have it, it's simple.

Difficulty: Medium. I found this one tough to frame, but easy to solve. I did take too much time.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2013

answer 19, answer 20.

So I enjoyed framing #20... Drawing 8 marbles is like lining 8 of them up... and the question asks for the probability that the last is yellow.... So that would be the rightmost? hmm, or the leftmost? No loss of generality left to right. And no loss of generality if we consider the last marble, or the first...

ReplyDeleteJonathan