instal the last version for ipod Drive SnapShot 1.50.0.1223

However, this puzzle asked for the average distance to the origin, which was defined as positive whether the grasshopper was to the left or to the right. So while the average position was always zero, the average distance to the origin was positive as soon as the grasshopper took its first jump. Suppose the grasshopper’s first jump was to the right, meaning it was now at 1/2.

Since subsequent jumps were equally likely to be left or right, its average position from this point forward remained at 1/2. What’s more, there was no way for the grasshopper to ever cross over to the left side of the origin again. Even if all the remaining jumps were to the left, the grasshopper would have been at 1/4, then 1/8, then 1/16 and so on, returning to the origin after infinitely many jumps. Because you never had to worry about crossing the origin again, the average distance the grasshopper had to travel was simply 1/2. Now suppose the grasshopper’s first jump was to the left, meaning it was now at -1/2. This time around, it could never return to positive territory, even if all the remaining jumps were to the right.

And so, once again, the average distance the grasshopper had to travel was simply 1/2.

Instal the last version for ipod Drive SnapShot 1.50.0.1223