Here is the missing part of the 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).
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.
Answer:
Thus, passing over Cuba alter the probability that Isaac would become a hurricane by the time it reached the Gulf of Mexico in the sense that passing over cuba tends to slow down Tropical storms. This further implies that the probability that Isaac would become a hurricane by the time it reached the Gulf of Mexico depreciates from 0.69 to 0.4701.
Explanation:
From the given information;
Let q represent the event that Isaac passes over cuba
Let R represent the event that Isaac become a hurricane by the time he reaches the Gulf of Mexico
Let S represent the event that Isaac does not become a hurricane and remains a Tropical storm when it reaches the Gulf of Mexico
P(R) = 0.69
PS) = 1 - P(R)
P(S) = 1 - 0.69
P(S) = 0.31
We know that ;
P (q/R) = 0.08
P(q/S) = 0.20
Then:
Therefore, passing over Cuba alter the probability that Isaac would become a hurricane by the time it reached the Gulf of Mexico in the sense that passing over cuba tends to slow down Tropical storms. This further implies that the probability that Isaac would become a hurricane by the time it reached the Gulf of Mexico depreciates from 0.69 to 0.4701.