A high school in a small town always has its homecoming day and parade on the first Saturday in October. From historical records, it has been determined that the probability of rain during the parade is 0.16. Amina will attend the high school for the next four years and plans to play in the marching band in the parade.(a)What is the probability that it will not rain on the homecoming parade in Amina's first year? (b)What is the probability that it will not rain on any of the homecoming parades during Amina's four years at the school? (Round your answer to three decimal places.) (c)What is the probability that it will rain on Amina's parade at least once during her four years of attendance? (Round your answer to three decimal places.)
Question
A high school in a small town always has its homecoming day and parade on the first Saturday in October. From historical records, it has been determined that the probability of rain during the parade is 0.16. Amina will attend the high school for the next four years and plans to play in the marching band in the parade.(a)What is the probability that it will not rain on the homecoming parade in Amina's first year? (b)What is the probability that it will not rain on any of the homecoming parades during Amina's four years at the school? (Round your answer to three decimal places.) (c)What is the probability that it will rain on Amina's parade at least once during her four years of attendance? (Round your answer to three decimal places.)
Solution
(a) The probability that it will not rain on the homecoming parade in Amina's first year is calculated by subtracting the probability of rain from 1. So, 1 - 0.16 = 0.84. Therefore, the probability is 0.84 or 84%.
(b) The probability that it will not rain on any of the homecoming parades during Amina's four years at the school is calculated by raising the probability of no rain in one year to the power of 4 (since there are 4 years). So, 0.84^4 = 0.498. Therefore, the probability is approximately 0.498 or 49.8% when rounded to three decimal places.
(c) The probability that it will rain on Amina's parade at least once during her four years of attendance is calculated by subtracting the probability of no rain in all four years from 1. So, 1 - 0.498 = 0.502. Therefore, the probability is approximately 0.502 or 50.2% when rounded to three decimal places.
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