A hotel guest satisfaction study revealed that 32% of hotel guests experienced better-than-expected quality of sleep at the hotel. Among these guests, 50% stated they would "definitely" return to that hotel brand.

a. Find the probability that 3 of the 14 hotel guests experienced a better-than-expected quality of sleep and would return to that hotel brand.

b. Find the probability that at least 3 of the 14 hotel guests experienced a better-than-expected quality of sleep and would return to that hotel brand.

c. Find the probability that at most 2 of the 14 hotel guests experienced a better-than-expected quality of sleep and would return to that hotel brand.

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