In August 2012, Tropical Storm Isaac formed in the Caribbean and was headed for
ID: 3205452 • Letter: I
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 0.69 that Isaac would become a hurricane by the time it reached the Gulf of Mexico. (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 storm was projected to pass directly over Cuba before reaching the Gulf of Mexico. Historically, the probability that a hurricane in the Gulf of Mexico had passed over Cuba is 0.08. The probability that a tropical storm in the Gulf of Mexico had passed over Cuba is 0.20. What would be the new probability that Isaac would become a hurricane knowing that it will pass over Cuba?Explanation / Answer
a) probabilty =1-P(Issac will become Hurrican) =1-0.69 =0.31
b)probability that it will pass over Cuba=P(A) =P( it will become hurrican&passed over cuba+it will remain tropical storm and pass over cuba) =0.69*0.08+0.31*0.2=0.1172
hence probabilty of it become Hurrican, given passes over cuba =0.69*0.08/0.1172 =0.471