SOLUTION: For the past 107 ​years, a certain state suffered 28 direct hits from major​ (category 3 to​ 5) hurricanes. What is the probability that the state will not be h

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Question 1127123: For the past 107 ​years, a certain state suffered 28 direct hits from major​ (category 3 to​ 5) hurricanes.
What is the probability that the state will not be hit by a single hurricane?
What is the probability that the state will be hit by at least one major hurricane in a single​ year?
Can you explain to me the steps to figuring this out ??
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
(a)
What is the probability that the state will not be hit by any major hurricanes in a single& year?
Solution:
Given Poisson distribution, assuming historical trends up to the last century still apply today.
Mean number of direct hits per year, lambda+=+28%2F107

PMF%28k%2Clambda%29=lambda%5Ek%2A%28%28e%5E%28-lambda%29%29%2Fk%21%29

k=0

PMF%280%2Clambda%29=lambda%5Ek%2A%28%28e%5E%28-lambda%29%29%2F0%21%29

=%2828%2F107%29%5E0%28%28e%5E%28-28%2F107%29%29%2F0%21%29

=1%2A%28%28e%5E%28-28%2F107%29%29%2F1%29

=e%5E%28-28%2F107%29

=0.7698


(b) What is the probability that the state will be hit by at least one major hurricane in a single year?


k%3E=1
P%28k%29=1-P%28k=0%29=1-0.7698=0.2302