Question 1137801: 2. A certain Area in the Philippines is, on the average, hit by 5 typhoons a year. Find the probability that in a given year, this are will be hit by:
A. fewer than 4 typhoons
B. anywhere from 3 to 5 typhoons
Answer by ikleyn(52777)   (Show Source):
You can put this solution on YOUR website! .
I just saw (and solved) several similar problems in this forum.
They are not exactly and precisely mathematical, since the condition is not completed and requires some additions.
Again, they are not exactly and precisely mathematical, but mostly serve to exercise your "common sense".
They require you to reformulate the condition in a way the problem to obtain its sense.
And they require such an addition
a) "to be consistent" with the given part, and
b) to be likelihood.
So, again, it is not "the pure Mathematics in its pure instance" - it is the common sense hypothesizing
to make right formulation and to get the problem solved ( = to get a likelihood solution ).
After this introduction, I can now move to the solution.
Having nothing else given, an appropriate hypotheses is to assume that we have random variable X = "the number of typhoons"
with integer random values which is uniformly distributed with the minimum value of 0 and the maximum value of 10.
Then the mean average is exactly 5, as the problem states, and the condition becomes "consistent with the given part" and "self-closed".
Then the answer to question (A) is P(X < 3) =  (X may have values of 0, 1, 2 or 3 of 11 possible integer values from 0 to 10);
the answer to question (B) is P(X= 3, or 4, or 5) =  .
Solved.
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See the lesson
- Unusual probability problems
in this site, where you will find many other similar problems solved and explained.
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