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).

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.


c. What happens to the probability of a storm becoming a hurricane when a tropical storm passes over a landmass such as Cuba? Increased or decreased from (to 2 decimals) to (to 4 decimals).

Answer 1

Answer:

A. 0.31

B. Probability of a hurricane decreases. (0.69 to 0.4709)

   Probability of a storm increases. (0.31 to 0.5290)

C. Decreased from 0.69 to 0.4709

Step-by-step explanation:

A. The probability Isaac becomes a hurricane is 0.69

    The probability of it NOT becoming a hurricane would then be: 1 - 0.69

    This is 0.31, which is the answer

B. Let's first take out the probabilities of a hurricane passing over Cuba, and a storm passing over Cuba. These are:

   Hurricane passing over Cuba: 0.69 * 0.08 = 0.0552

   Tropical Storm passing over Cuba: 0.31 * 0.2 = 0.062

Since it is already given that the hurricane / tropical storm is passing over Cuba, the only probabilities we need to consider are the one's we just calculated above.

  Total probability : 0.0552 + 0.062 = 0.1172

  New probability of hurricane, given it passes over Cuba: $\frac{0.0552}{0.1172} = 0.4709$

  New probability of storm, given it passes over Cuba: $\frac{0.062}{0.1172} = 0.5290$

C. Initial probability of storm becoming a hurricane: 0.69

   Probability of storm becoming a hurricane, given it passes over             Cuba: 0.4709

   Thus we can see the probability decreases from 0.69 to 0.4709.