April 2007 IBM Ponder This Challenge

[pzhon]

Many reading this forum may like this month's Ponder This challenge from IBM, which can be viewed as a probability problem:
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This month's puzzle concerns a frog who is hopping on the integers from minus infinity to plus infinity. Each hop is chosen at random (with equal probability) to be either +2 or -1. So the frog will make steady but irregular progress in the positive direction. The frog will hit some integers more than once and miss others entirely. What fraction of the integers will the frog miss entirely? Please find an exact answer.[/list]