Assume a category 3 hurricane has a probability of 0.01 to upgrade to a category

Question

Assume a category 3 hurricane has a probability of 0.01 to upgrade to a category 4 category hurricane. You are tracking the progression of category 3 hurricanes. You have collected data about 2557 hurricanes that occurred in the past 150 years, among which 538 started as a category 3 hurricane. Use this information and answer questions 3a to 3h. Question 3e: What is the probability that there are more than two category 3 hurricanes upgraded to category 4 hurricanes in the data that you collected? (Use 3 decimal places) Question 3f You randomly select a subset of 20 hurricanes from a group of hurricanes which started as a category 3. Of these 20 hurricanes, two hurricanes actually turned into a category 4 hurricane. This is a(n): O Sample space Outcome O Event Probability

Explanation / Answer

The answer to the question is as follows:

3e.

This is essentialy given by :

P(X>2) = 1-P(X<2) = 1- (538C0 (.01^0)*.99^538 + 538C1 (.01^1)*.99^537 ) = 0.9051

3f.

Sample space is basically all possible outcomes of a variable - answer can't be this

An outcome is the result of a random experiment, like a rolling a die has six possible outcomes (say) - this is not the answer

However, an "event" is a set of outcomes to which a probability is assigned. One possible event is "rolling a number less than 3" - this fits as answer, because have a event defined here ( whichis basically out of the 20 sampled, hurricanes turning from cat 3 to cat 4)

Probability is the chance of 1 event happening - not the answer

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