question archive If a hurricane forms in the eastern half of the Gulf of Mexico, there is a 76 percent chance that it will strike the western coast of Florida
If a hurricane forms in the eastern half of the Gulf of Mexico, there is a 76 percent chance that it will strike the western coast of Florida
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If a hurricane forms in the eastern half of the Gulf of Mexico, there is a 76 percent chance that it will strike the western coast of Florida. From data gathered over the past 50 years, it has been determined that the probability of a hurricane's occurring in this area in any given year is 0.85.
(a) What is the probability that a hurricane will occur in the eastern Gulf of Mexico and strike Florida this year?
(b) If a hurricane in the eastern Gulf of Mexico is seeded (induced to rain by addition of chemicals from aircraft), its probability of striking Florida's west coast is reduced by one-fourth. If it is decided to seed any hurricane in the eastern gulf, what is the new value for the probability in part (a)?
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Answer:
Let S: strike the westren coast of florida and H:Hurricane will occur
We are given that P(S|H) = 0.76 and P(H) = 0.85
a) To find the probabliy that a hurricane will occur in the eastern gulf of mexico and strike florida this year.That is P( H and S) =P(S and H)
Using conditional probability formula , P(S|H) = P( S and H)/P(H)
Which gives , P(S and H) = P(S|H)*P(H) = 0.76*0.85= 0.646
b) It is given that , if a hurricane is seeded, then probability of striking is reduced by one-fourth of 76% = 0.76*0.25 =0.19
So reduced probability P( S|H)= 0.76-0.19= 0.57
P(S and H) = P(S|H)*P(H) = 0.57*0.85= 0.4845
