Question

the probability that a certain state will be hit by a major tornado (category f4 or f5) in any single year is $\frac{1}{17}$. complete parts (a) through (d) below.
a. what is the probability that the state will be hit by a major tornado two years in a row?
(simplify your answer. round to five decimal places as needed.)

Explanation:

Step1: Determine the probability of independent events

The probability of being hit by a major tornado in one year is \( p=\frac{1}{17} \). Since the events (tornado in year 1 and tornado in year 2) are independent, we use the formula for the probability of independent events \( P(A\cap B)=P(A)\times P(B) \).

Step2: Calculate the probability

Let \( A \) be the event of a tornado in the first year and \( B \) be the event of a tornado in the second year. Then \( P(A) = P(B)=\frac{1}{17} \). So \( P(A\cap B)=\frac{1}{17}\times\frac{1}{17}=\frac{1}{289}\approx0.00346 \)

Answer:

\( 0.00346 \)