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 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 flooding when there is one hurricane, (iii probability of no flooding when there are two hurricanes, iv) Use theorem of total probability to calculate probability of no flooding.]

Explanation / Answer

probability that local school will not be flooded flooded=P( 0 hurricanes and not flooded +1 hurricane and not flooed+

2 hurricane and not flooded)=0.75*1+0.20*(1-0.60)+0.05*(1-0.60)*(1-0.60)=0.838

please revert for any clarification required

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