Two natural events can result in the failure of a dam. Firstly, a very high flood, exceeding the design capacity of its spillway (event A), may destroy it. Secondly, a destructive earthquake (event B) can cause a structural collapse. Let P[A] = 0.04 and P[B]=0.02 denote the respective probabilities of occurrence in a year. If the two events are statistically independent, what is the risk of failure of the dam in a year?

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Originally Posted by urdream

Two natural events can result in the failure of a dam. Firstly, a very high flood, exceeding the design capacity of its spillway (event A), may destroy it. Secondly, a destructive earthquake (event B) can cause a structural collapse. Let P[A] = 0.04 and P[B]=0.02 denote the respective probabilities of occurrence in a year. If the two events are statistically independent, what is the risk of failure of the dam in a year?

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If two events are independent, they can not be mutually exclusive.

P(A or B) = P(A)+P(B)-P(A and B)

galactus, would be a pretty bad day if you have a huge flood on the day of a terrible earthquake though. Maybe that's just too horrible to consider :)

It certainly has happened. Case in point, the terrible tsunami which struck Asia a few years back. That was brought on by an earthquake.