The probability that a certain state will be hit by a major tornado (category \( \mathrm{F4} \) 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 consecifive years? 0.00800 (Simplify your answer. Round to five decimal places as needed.) c. What is the probability that the state will not be hit by a major tornado in the next ten years? \( \square \) (Round to three decimal places as needed.)

The probability that the state will not be hit by a major tornado in any single year is \( 1 - \frac{1}{5} = \frac{4}{5} \). To find the probability that the state will not be hit by a major tornado in the next ten years, we take the probability of not being hit in one year and raise it to the power of ten: \[ P(\text{not hit in 10 years}) = \left(\frac{4}{5}\right)^{10} \approx 0.10737 \] Thus, rounding to three decimal places, the probability is approximately \( 0.107 \). In a broader context, major tornadoes are relatively rare natural disasters, which can make predicting their occurrence challenging. Factors like geography, time of year, and climatic changes can influence the likelihood of such extreme weather events. Understanding these probabilities helps governments and organizations prepare for emergency management plans to minimize risks and protect lives. Furthermore, the concept of probability provides practical applications beyond just tornadoes. From predicting sports outcomes to estimating risks in financial markets, probability teaches us how to make informed decisions based on uncertain events, enhancing our problem-solving skills in everyday life.