Beginner statistics question? Please help!! What formula should I use? How should I solve this?

Question

Florida Hurricanes: The following distribution for X = annual number of hurricanes in the state of Florida was reported in an article entitled “What Seasonal Hurricane Forecasts Mean to Florida”.

X=# of hurricanes, Annual Probability
0                        , 0.60
1                        , 0.30
2                        , 0.07
3                        , 0.02
4                        , 0.01

Given that two hurricanes have already occurred and the year is not yet over, what is the probability that there will actually be a total of three hurricanes in all?

The right answer is 0.20, but how do I solve it?

 

Answer 1

Since 2 hurricanes have already happened we can try to construct a new probability distribution that looks like:

 

X        Q(X)

----------------

0       0.00

1       0.00

2       0.7

3       0.2

4       0.1

 

P(0) and P(1) = 0 now because based on the given info they did not happen.

 

However the remaining probabilities must be adjusted to add up to one since the new "sample space" is {2,3,4}

 

Q(2) = P(2)/P(2 or 3 or 4) = .07/.1 = .7

Q(3) = P(3)/P(2 or 3 or 4) = .02/.1 = .2

Q(4) = .01/.1 = .1

 

 

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