The following are the probabilities for occurence of hurricane in a neighborhood

Question

The following are the probabilities for occurence of hurricane in a neighborhood next year - 0.75 for no occurence, 0.20 for one occurence, and 0.05 for two occurences. The chances of three or more hurricanes happening in a year is zero. If a hurricane occurs, then there is a 60 % chance that the local school will be flooded. Assume that the events corresponding to flooding of local school from each hurricane event is independent. Assume that there are no other causes of flooding in school other than hurricanes. What is the probability that the local school will not be a flooded next year? Hint: Determine the following: (i) probability of no flooding given that there are zero hurricane, (ii)probability of no looding when there is one hurricane,) probability of no flooding when there are two hurricanes, (iv) Use theorem of total probability to calculate probability of no flooding. Question 4 The intensity of load on a tower due to wind during a hurricane can be either high (H) or medium (M). The duration of the load can be long (L) or short (S). If the duration of load is long, then the probability of it being high is 0.6. If the intensity of load is high, then the probability of duration being short is 0.3. The probability of long duration load occuring during a hurricane is 0.2 Determine the probability of duration of load being long given that the intensity of load is high? Determine the probability of duration of load being long and the intensity of load is high? Determine the probability of load being high intensity?

Explanation / Answer

question 4.

P(H|L) = 0.6 and P(H|L') = 0.4
P(S|H) = 0.3 and P(S|H') = 0.7
P(L) = 0.2 and P(L') = 0.8

P(L|H) = P(H|L)*P(L) / (P(H|L)*P(L) + P(H|L')*P(L')) = 0.6*0.2 / (0.6*0.2 + 0.4*0.8) = 0.2727

P(L and H) = P(H|L)*P(L) = 0.6*0.2 = 0.12

P(H) = P(H|L)*P(L) + P(H|L')*P(L') = 0.6*0.2 + 0.4*0.8 = 0.44

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