Question

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) Let H-event Isaac becomes a hurricane by the time it reaches the Gulf of Mexico. T event Isaac does not become a hurricane and remains a tropical storm when it reaches the Gulf of Mexico. σ-event that Isaac passes over Cuba. a. What was the probability that Isaac would not become a hurricane but remain a tropical storm when it reached the Gulf of Mexico (to 2 decimals)? b. Two days later, the National Hurricane Center projected the path of Isaac would pass directly over Cuba before reaching the Gulf of Mexico. 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. 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 above probabilities to answer this question. (to 2 decimals) (to 2 decimals) (to 4 decimals) P(CIT) c. What happens to the probability of becoming a hurricane when a tropical storm passes over a landmass such as Cuba? -Select your answerto2 decimals) to(to 4 decimals) ls) to。(to

Answer 1

(a)

From the given information we have

P(H) = 0.69

By the complement rule,

(b)

From given information we have

P(C|H) = 0.08

P(C|T) = 0.20

By the law of total probability we have

P(C) = P(C|H) P(H) + P(C|T)P(T) = 0.08 * 0.69 + 0.20 * 0.31 = 0.1172

So

P(H |C) = [ P(C|H)P(H) ] / P(C)= [ 0.08*0.69] / 0.1172 = 0.4710

(c)

reduces from 0.69 to 0.4710.