A specific coffer dam has a probability of 0.05 of being overtopped by a flood i

Question

A specific coffer dam has a probability of 0.05 of being overtopped by a flood in any 1 week.  

We are interested in the probability that the first overflow will not occur until the xth week.   

(a) What is the probability that the first overtopping occurs in week 6?  

(b) How many weeks are we expecting to have the first overtopping?  

(c) What is the probability that the dam will not be overtopped in a 2-year period (104  

weeks)?  

(d) How many number of overtopping are we expecting in a 2-year (104 weeks) period?

Iknow this is about discrete variables but Im not sure how toapproach it. Please help. Answers will be rated

Explanation / Answer

I repeated and independent with sucess being p then the thedistribution of X the number of trials until the first success isgiven by f(x)=p(1-p)x-1    fox x=1,... and E[p]=1/p In this case p=.05 a)P(X=6)=.05(.95)5=.038689 b)E[X]=1/p=20 weeks c)The probabilty that the first overtap occurs after week 104is equal to P(0 overtops in 104weeks)=C(104,0)p0(1-p)104=,004822 d)Expected overtops in 104 weeks=104(.05)=5.2 overtops d)

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