Question: Joe is throwing rocks at a plastic bottle floating in the middle of a pond. Suppose that the probability that he hits the bottle is equal to 0.5 and results of different throws are all independent. He makes a total of 10 throws.

1. What is the probability that he hits the bottle at least 3 times?
2. What is the probability that he misses on the first and last throws and hits it exactly 5 times in total?
3. What is the probability that he misses all 10 times?
4. What is the probability that he hits it exactly five times in a row and misses all other attempts?

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