Poor Frog

There is a frog stuck in a 10 feet deep well. Every day in the morning he jumps up 3 feet, and at night slides down 1. Each night there is a 50% chance that there is a 50% chance of rain, and a 50% chance that there is no chance of rain. When it rains, the poor frog slides down an additional 1 feet. What is the probability that the frog would escape in 5 days?

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