In a particular area, 40% of soil samples show excessive levels of lead, while 3

Question

In a particular area, 40% of soil samples show excessive levels of lead, while 30% show excessive levels of chromium, and 10% have excessive levels of both. If another soil sample is taken in the same area,

(a) (6 points) what is the probability that the sample will have excessive levels of lead or chromium?

b) (6 points) what is the probability that lead will not appear at excessive levels?

(c) (7 points) what is the probability that neither metal appears at excessive levels?

(d) (6 points) A cleanup process is being suggested, where the soil is washed using a neutralizing binding solution. However, it is estimated that 80% of those soils with excessive level of both metals will fail to be cleaned using this simple procedure and must be put through a much more expensive process. What fraction of the soil is likely to need the more expensive process?

Explanation / Answer

probailty of lead=P(L)=0.4

and that of Chromium =P(C)=0.3

and for both P(LnC)=0.1

hence a) probability that the sample will have excessive levels of lead or chromium=P(LUC)=P(L)+P(C)-P(LnC)

=0.4+0.3-0.1=0.6

b)probability that lead will not appear at excessive levels=1-P(L)=1-0.4=0.6

c)probability that neither metal appears at excessive levels=1-P(LUC)=1-0.6=0.4

d)fraction of the soil is likely to need the more expensive process =0.8*P(LnC)=0.8*0.1=0.08

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