A specific coffer dam has a probability of 0.05 of beingovertopped by a flood in

Question

A specific coffer dam has a probability of 0.05 of beingovertopped by a flood in any 1 week. We are interested in theprobability that the first overflow will not occur until the xthweek. (a) What is the probability that the first overtopping occursin week 6? (b) How many weeks are we expecting to have the firstovertopping? (c) What is the probability that the dam will not beovertopped in a 2-year (104 weeks) period? (d) How many numbers of overtoppings are we expecting to havein a 2-year period? *Note: i have already solved (a) and (c) and found the answersto be 0.0387 for (a) and 0.0048 for (c). So i just need help with(b) and (d). Any help would be greatly appreciated and rated well.Thanks! A specific coffer dam has a probability of 0.05 of beingovertopped by a flood in any 1 week. We are interested in theprobability that the first overflow will not occur until the xthweek. (a) What is the probability that the first overtopping occursin week 6? (b) How many weeks are we expecting to have the firstovertopping? (c) What is the probability that the dam will not beovertopped in a 2-year (104 weeks) period? (d) How many numbers of overtoppings are we expecting to havein a 2-year period? *Note: i have already solved (a) and (c) and found the answersto be 0.0387 for (a) and 0.0048 for (c). So i just need help with(b) and (d). Any help would be greatly appreciated and rated well.Thanks!

Explanation / Answer

(a) the probability that the first overtopping occurs in week6 = 0.95*0.95*0.95*0.95*0.95*0.05 =0.039


(c) the probability that the dam will not be overtopped in a2-year (104 weeks) period =0.95 ^ 104 =0.0048

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