Question

Below in bold (part B) is where I need help and a detailed explaination of where and why those numbers where used, please and thank you.

In August , tropical storm Isaac formed in the Caribbean and was headed for the Gulf of Mexico. There was an initial probability of that Isaac would become a hurricane by the time it reached the Gulf of Mexico (National Hurricane Center website, August , ). Let event Isaac becomes a hurricane by the time it reaches the Gulf of Mexico. event Isaac does not become a hurricane and remains a tropical storm when it reaches the Gulf of Mexico. 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 decimals)? .31

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 probability of having passed over Cuba. Tropical storms that reach the Gulf of Mexico have a 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?

*** PLEASE PROVIDE DETAIL ANSWER TO 3 FORMULA BELOW, SHOWING WHAT NUMBERS WERE USED AND WHERE THEY CAME FROM. ALL STEPS PLEASE***

P(C/H)= (2 DECIMALS)

P(C/T)= (2 DECIMALS)

P(H/C)= (4 DECIMALS)

Use the above probabilities to answer this question. (to decimals) (to decimals) (to decimals) c. What happens to the probability of becoming a hurricane when a tropical storm passes over a landmass such as Cuba? .69 (to decimals) to .4710 (to 4 decimals).

Answer 1

Compute the probability that Isaac would not become hurricane.

Probability 1P(Issac will become Hurrican) -1-0.69 - 0.31

Probability that Isaac would not become a hurricane but remain a tropical storm when it reached the Gulf of Mexico is 0.31.

Suppose there was an initial probability of 0.69 that Isaac would become a hurricane.

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 of 3

Consider that:

A the event Isaac would become a hurricane. c J the event Isaac would not become a hurricane but remain a tropical storm.

The event Isaac would pass over Cuba before\ reaching the Gulf of Mexico

It is given in the problem that,

P(B|A) 0.08
and
P(BIA")-0.20

P(A) 0.69
and
r(A")-0.31

So, the required probability by using Baye’s Theorem is given as below:

0.69 x 0.08+0.31x0.20 0.1172

Probability that Isaac would become a hurricane by the time it reached the Gulf of Mexico is 0.1172.

Explanation

Probability that Isaac would become a hurricane by the time it reached the Gulf of Mexico is 0.1172.

Step 3 of 3

Compute the probability of becoming a hurricane when a tropical storm passes over a landmass such as Cuba.

Probability that Isaac would become a hurricane but remain a tropical storm when it reached the Gulf of Mexico is 0.69.

Therefore, the probability of becoming a hurricane when a tropical storm passes over a landmass such as Cuba decreased from 0.69 to 0.4710.

Probability of becoming a hurricane when a tropical storm passes over a landmass such as Cuba is 0.4710.

Probability of becoming a hurricane when a tropical storm passes over a landmass such as Cuba decreased from 0.69 to 0.4710

Explanation

Probability of becoming a hurricane when a tropical storm passes over a landmass such as Cuba is 0.4710.

Probability that Isaac would become a hurricane but remain a tropical storm when it reached the Gulf of Mexico is 0.69. Therefore, the probability of becoming a hurricane when a tropical storm passes over a landmass such as Cuba decreased from 0.69 to 0.4710.

Answer

Probability that Isaac would not become a hurricane but remain a tropical storm when it reached the Gulf of Mexico is 0.31.

Probability that Isaac would become a hurricane by the time it reached the Gulf of Mexico is 0.1172.

Probability of becoming a hurricane when a tropical storm passes over a landmass such as Cuba is 0.4710.

Probability of becoming a hurricane when a tropical storm passes over a landmass such as Cuba decreased from 0.69 to 0.4710