(4) (Preview of binomial distribution) Suppose the safe criterion for arsenic in

Question

(4) (Preview of binomial distribution) Suppose the safe criterion for arsenic in fresh water is less than 340 g/L. Suppose you want to test the water in 5 wells spread out far enough from each other that a hydrogeologist has confirmed that the 5 wells are drawing from different aquifers (and hence testing should be independent). If the probability of a water sample being clean enough for drinking (i.e., a success) is p: » What is the probability that all 5 tests were successful? » What is the probability that none of the tests were successful? » What is the probability that one of the tests was successful? » What is the probability that two of the tests were successful? . What is the probability that n of the tests were successful, where 0 Sn

Explanation / Answer

Ans:

Binomial distribution with parameter n=5,probability of success=p

P(x=k)=5Ck*pk*(1-p)5-k

k=0,1,2,3,4,5

1)P(all)=P(x=5)=5C5*p5*(1-p)0=p5

2)P(none)=P(x=0)=5C0*p0*(1-p)5-0=(1-p)5

3)P(x=1)=5C1*p1*(1-p)5-1=5p(1-p)4

4)P(x=2)=5C2*p2*(1-p)3=10p2(1-p)3

5)P(x=n)=5Cn*pn*(1-p)5-n

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