1- The probability that a certain state will be hit by a major tornado (category F4 or F5) in any single year is \( \frac{1}{5} \). Complete parts (a) through (d) below. a. What is the probability that the state will be hit by a major tomado two years in a row? 0.04000 (Simplify your answer. Round to five decimal places as needed.) b. What is the probability that the state will be hit by a major tomado in three consecutive years? 0.00800 (Simplifify your answer. Round to five decimal places as needed.) c. What is the probability that the state will not be hit by a major tomado in the next ten years? 0.107 (Round to three decimal places as needed.) d. What is the probability that the state will be hit by a major tomado at least once in the next ten years? \( \square \) (Round to three decimal places as needed.)
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To calculate the probability that the state will be hit by a major tornado at least once in the next ten years, we can use the complement rule. First, let's determine the probability that the state will not be hit by a major tornado in any given year, which is \(1 - \frac{1}{5} = \frac{4}{5}\). Now we want the probability that the state will not be hit for ten consecutive years: \((\frac{4}{5})^{10} \approx 0.1074\) (Rounded to three decimal places: 0.107). Lastly, the probability that it will be hit at least once in ten years is the complement of not being hit at all: \(1 - P(\text{not hit}) = 1 - 0.107 \approx 0.893\) So, rounding to three decimal places, the answer is approximately **0.893**.
