MathDB

On a certain planet, the alien inhabitants are born without any arms, legs, or noses. Every year, on their birthday, each alien randomly grows either an arm, a leg, or a nose, with equal probability for each. After its sixth birthday, the probability that an alien will have at least

2

arms, at least

2

legs, and at least

1

nose on the day is

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. Compute

m + n

Problem Statement