In August 2012, tropical storm Isaac formed in the Caribbean and was headed for the Gulf of Mexico. There was an initial probability of .69 that Isaac would become a hurricane by the time it reached the Gulf of Mexico (National Hurricane Center website, August 21, 2012). a. What was the probability that Isaac would not become a hurricane but remain a tropical storm when it reached the Gulf of Mexico? b. Two days later, the National Hurricane Center projected the path of Isaac would pass directly over Cuba before reaching the Gulf of Mexico. How did passing over Cuba alter the probability that Isaac would become a hurricane by the time it reached the Gulf of Mexico? Use the following probabilities to answer this question. Hurricanes that reach the Gulf of Mexico have a .08 probability of having passed over Cuba. Tropical storms that reach the Gulf of Mexico have a .20 probability of having passed over Cuba. c. What happens to the probability of becoming a hurricane when a tropical storm passes over a landmass such as Cuba?

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In August 2012, tropical storm Isaac formed in the Caribbean and was headed for the Gulf of Mexico. There was an initial probability of .69 that Isaac would become a hurricane by the time it reached the Gulf of Mexico (National Hurricane Center website, August 21, 2012).   a. What was the probability that Isaac would not become a hurricane but remain a tropical storm when it reached the Gulf of Mexico?   b. Two days later, the National Hurricane Center projected the path of Isaac would pass directly over Cuba before reaching the Gulf of Mexico.  How did passing over Cuba alter the probability that Isaac would become a hurricane by the time it reached the Gulf of Mexico? Use the following probabilities to answer this question. Hurricanes that reach the Gulf of Mexico have a .08 probability of having passed over Cuba. Tropical storms that reach the Gulf of Mexico have a .20 probability of having passed over Cuba.   c. What happens to the probability of becoming a hurricane when a tropical storm passes over a landmass such as Cuba?

soniarus7x · Accepted Answer

Step 1  (a). Find the probability that Isaac would not become a hurricane but remain a tropical storm when it reached the Gulf of Mexico:  Denote the event that “Isaac would become a hurricane by the time it reached the Gulf of Mexico” as A.  It is given that, the initial probability of .69 that Isaac would become a hurricane by the time it reached the Gulf of Mexico. That is, P(A)=0.69.  Denote the event that “Isaac would not become a hurricane but remain a tropical storm when it reached the Gulf of Mexico” as Ac.  The probability that Isaac would not become a hurricane but remain a tropical storm when it reached the Gulf of Mexico is obtained as 0.31 from the calculation given below:  P(Ac)=1−P(A)=1−0.69  =0.31  Thus, the probability that Isaac would not become a hurricane but remain a tropical storm when it reached the Gulf of Mexico is 0.31.  Step 2  (b). Find the probability that Isaac would become a hurricane by the time it reached the Gulf of Mexico while passing over Cuba:  Denote the event that “The path of Isaac would pass directly over Cuba before reaching the Gulf of Mexico” as B.  It is given that, Hurricanes that reach the Gulf of Mexico have a .08 probability of having passed over Cuba. That is, P(B∣A)=0.08.  It is also given that, Tropical storms that reach the Gulf of Mexico have a .20 probability of having passed over Cuba. That is, P(B∣Ac)=0.2.  The probability that Isaac would become a hurricane by the time it reached the Gulf of Mexico while passing over Cuba is obtained as 0.1172 from the calculation given below:  P(B)=P(A)×P(B∣A)+P(Ac)×P(B∣Ac)  =0.69×0.08+0.31×0.2  =0.0552+0.062  =0.1172  Thus, the probability that Isaac would become a hurricane by the time it reached the Gulf of Mexico while passing over Cuba is 0.1172.  (c). Find the probability of becoming a hurricane when a tropical storm passes over a landmass such as Cuba:   The probability of becoming a hurricane when a tropical storm passes over a landmass such as Cuba is obtained as 0.4710 from the calculation given below:  P(A∣B)=P(A∩B)P(B)  =P(A)×P(B∣A)P(B)  =0.69×0.080.1172  =0.05520.1172  =0.4710  Thus, the probability of becoming a hurricane when a tropical storm passes over a landmass such as Cuba is 0.4710.

In August 2012, tropical storm Isaac formed in the Caribbean and was h

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