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? \( \square \) (Simplify your answer. Round to five decimal placesjas needed.)

To calculate the probabilities for parts (a) and (b), we can use the information given that the probability of being hit by a major tornado in any single year is \( \frac{1}{5} \). For part (a): The probability that the state will be hit by a major tornado two years in a row is calculated as follows: \[ P(\text{2 years}) = P(\text{hit in year 1}) \times P(\text{hit in year 2}) = \frac{1}{5} \times \frac{1}{5} = \frac{1}{25} = 0.04000 \] Now for part (b): The probability that the state will be hit by a major tornado in three consecutive years is calculated in a similar way: \[ P(\text{3 years}) = P(\text{hit in year 1}) \times P(\text{hit in year 2}) \times P(\text{hit in year 3}) = \frac{1}{5} \times \frac{1}{5} \times \frac{1}{5} = \frac{1}{125} = 0.00800 \] So, the answer for part (b) is: 0.00800 (Simplifying this shows it is \( \frac{1}{125} \), which rounds to five decimal places as needed).