For a county in Texas, the probabilities that it will be hit by one or two hurri

Question

For a county in Texas, the probabilities that it will be hit by one or two hurricanes each year are 0.3 and 0.05, respectively. The event that it will be hit by three or more hurricanes in a year may be assumed to have negligible probability This county may be subjected to floods each year from the melting of snow in the upstream regions, or from the heavy precipitation brought by hurricanes, or both. Normally, the chance of flood in a year, caused by the melting snow, is 10%. However, during a hurricane, there is a 25% probability of flooding. Assume that floods caused by the melting snow and floods caused by hurricanes are statistically independent events. What is the probability that there will be flooding in this county in a year?

Explanation / Answer

P(1 hurricane) = 0.3

P(2 hurricanes) =0.05

P(Flooding caused by melting of snow) = 0.1

P(Flooding caused by hurricane) = 0.25

P(flooding this year) = P(Flooding caused by melting of snow) + P(Flooding caused by 1 hurricane) + P(Flooding caused by 2 hurricane)

= 0.1+0.3*0.25 +0.05*0.25 = 0.1875

That is 18.75% chances of flooding

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