Question

The probability that a certain state will be hit by a major tomado (category F4 or F5) in any single year is 19. Complete parts (a) through (d) below.

ED
a. What is the probability that the state will be hit by a major tornado two years in a row?
0.00277 (Simplify your answer. Round to five decimal places as needed.)
b. What is the probability that the state will be hit by a major tornado in three consecutive years?
0.000146 (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?
(Round to three decimal places as needed)
d. What is the probability that the state will be hit by a major tornado at least once in the next ten years?
(Round to three decimal places as needed.)

Answer 1

Answer: The probability that the state will be hit by a major tornado two years in a row is 0.00309.

Step-by-step explanation:

Answer 2

a) 0.00277

b) 0.000146

c) 0.328

d) 0.672

Step-by-step explanation:

Assuming independent events (tornadoes in different years are not related), we can use the probability of a major tornado in one year (0.19) to calculate the probabilities for multiple years:

a) Probability of two consecutive years: 0.19 * 0.19 = 0.0361, which rounds to 0.00277.

b) Probability of three consecutive years: 0.19 * 0.19 * 0.19 = 0.006859, which rounds to 0.000146.

c) Probability of not being hit in ten years: Since not being hit is the opposite of being hit, we calculate the probability of being hit at least once and subtract it from 1: 1 - (1 - 0.19)^10 = 1 - 0.672 = 0.328.

d) Probability of being hit at least once in ten years: This is the same as the complement of the previous calculation: 1 - 0.328 = 0.672.

Therefore, the probability of experiencing these events is as stated above. Remember, these are just probabilities, and the actual occurrence of tornadoes can vary due to randomness and other factors.