A particular Land Trust Organization is collecting information about the use of

Question

A particular Land Trust Organization is collecting information about the use of land in a particular county and whether it is conserved for environmental purposes and the degree of that conservation.   GAP status codes classify areas into highly protected, moderately protected (conserved but mainly used for other purposes), and unprotected. From the last survey, we know that 67% of the county is unprotected and 18% is highly protected. From the highly protected areas, 88% is forest and the rest is equally divided between urban use and agriculture use. Most of the unprotected land is used for urban purposes--85%. Twelve percent of what is moderately protected is forest. The rest of the moderately protected land is equally used for agriculture and urban purposes. We also know that the total amount of land used for agriculture in the county is 14%. Use four decimal places in the chart for this problem.  

4. Given that the parcel is somehow protected (either highly protected or moderately), what is the probability that this parcel is used for agriculture or is an urban area?

Explanation / Answer

We have the probabilities as :

Required probability =  Probability that this parcel is used for agriculture or is an urban area given parcel is somehow protected (either highly protected or moderately)

= P(parcel is used for agriculture or is an urban area / parcel is somehow protected)

= P(parcel is used for agriculture or is an urban area and parcel is somehow protected) / P(parcel is somehow protected)

P(parcel is used for agriculture or is an urban area and parcel is somehow protected) =

= 0.0108 + 0.0108 + 0.066 + 0.066 = 0.1536

P(parcel is somehow protected) = 0.18 + 0.15 = 0.33

Required probability = P(parcel is used for agriculture or is an urban area and parcel is somehow protected) / P(parcel is somehow protected)

= 0.1536 / 0.33 = 0.4655

Forest agriculture urban Total Highly protected 0.1584 0.0108 0.0108 0.18 Moderately protected 0.018 0.066 0.066 0.15 Unprotected 0.0373 0.0632 0.5695 0.67 Total 0.2137 0.14 0.6463 1

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