Question Find the probability that a state will be hit by a major tornado ( $\mathrm{F} 4$ or F5) two years in a row, given the probability of a major tornado in any single year is $\frac{1}{9}$ . Round the answer to five decimal places.

Studdy Solution

STEP 1

Assumptions1. The probability of the state being hit by a major tornado in any single year is $\frac{1}{9}$ . . The events of the state being hit by a major tornado in each year are independent.
3. We want to find the probability that the state will be hit by a major tornado two years in a row.

STEP 2

For independent events, the probability of both events occurring is the product of their individual probabilities. So, we can calculate the probability of the state being hit by a major tornado two years in a row by multiplying the probability of it being hit in one year by itself.
$(\text{hit two years in a row}) =(\text{hit in one year}) \times(\text{hit in one year})$

STEP 3

Now, plug in the given probability for the state being hit in one year to calculate the probability of it being hit two years in a row.
$(\text{hit two years in a row}) = \frac{1}{9} \times \frac{1}{9}$

STEP 4

Calculate the probability of the state being hit by a major tornado two years in a row.
$(\text{hit two years in a row}) = \frac{1}{9} \times \frac{1}{9} = \frac{1}{81}$

STEP 5

Finally, we need to round the probability to five decimal places as needed. The decimal representation of $\frac{1}{81}$ is approximately $0.012345679$ , which rounded to five decimal places is $0.01235$ .
$(\text{hit two years in a row}) =0.01235$ The probability that the state will be hit by a major tornado two years in a row is $0.01235$ .

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