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The Hiking Club plans to go camping in a State park where the probability of rain on any given day is 3//7. What is the probability that it will rain on exactly zero of the five days they are there? Round your answer to the nearest thousandth. Answer:

The Hiking Club plans to go camping in a State park where the probability of rain on any given day is 3/7 3 / 7 . What is the probability that it will rain on exactly zero of the five days they are there? Round your answer to the nearest thousandth.\newlineAnswer:

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Q. The Hiking Club plans to go camping in a State park where the probability of rain on any given day is 3/7 3 / 7 . What is the probability that it will rain on exactly zero of the five days they are there? Round your answer to the nearest thousandth.\newlineAnswer:
  1. Understand and Determine Probability: Understand the problem and determine the probability of the event not happening (no rain) on a single day.\newlineThe probability of rain on any given day is 37\frac{3}{7}, so the probability of no rain on any given day is 1−37=471 - \frac{3}{7} = \frac{4}{7}.
  2. Calculate Probability Over Five Days: Calculate the probability of no rain over the course of five days. Since each day is independent, we multiply the probability of no rain on each day together: (47)×(47)×(47)×(47)×(47)(\frac{4}{7}) \times (\frac{4}{7}) \times (\frac{4}{7}) \times (\frac{4}{7}) \times (\frac{4}{7}).
  3. Perform Calculation: Perform the calculation.\newline(47)×(47)×(47)×(47)×(47)=(4575)=102416807(\frac{4}{7}) \times (\frac{4}{7}) \times (\frac{4}{7}) \times (\frac{4}{7}) \times (\frac{4}{7}) = (\frac{4^5}{7^5}) = \frac{1024}{16807}.
  4. Round to Nearest Thousandth: Round the answer to the nearest thousandth.\newline1024/16807≈0.06091024 / 16807 \approx 0.0609 when rounded to the nearest thousandth.

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