2020 CIME II Problems/Problem 6
Revision as of 14:31, 6 February 2023 by Mathboy100 (talk | contribs) (Created page with "==Problem== An infinite number of buckets, labeled <math>1</math>, <math>2</math>, <math>3</math>, <math>\ldots</math>, lie in a line. A red ball, a green ball, and a blue bal...")
Problem
An infinite number of buckets, labeled 
, 
, 
, 
, lie in a line. A red ball, a green ball, and a blue ball are each tossed into a bucket, such that for each ball, the probability the ball lands in bucket 
is 
. Given that all three balls land in the same bucket 
and that is even, then the expected value of can be expressed as 
, where 
and 
are relatively prime positive integers. Find 
.
