One method to distinguish between granitic G and basaltic B

One method to distinguish between granitic (G) and basaltic (B) rocks is to examine a portion of the infrared spectrum of the sun\'s energy reflected from the rock surface. Let R1, R2, and R2 denote measured spectrum intensities at three different wavelengths; typically, for granite R1

Solution

(a) P(G|R₁<R₂<R₃) = 0.7*0.6=0.42

    P(B| R₁<R₂<R₃) = 0.45*0.4 = 0.18

Therefore, P(G|R₁<R₂<R₃)> P(B| R₁<R₂<R₃)

Rock will be classified as granite.

(b) If measurements yielded R₁<R₃<R₂, We would classify the rock as basalt as P(B|R₁<R₃<R₂) = 0.5*0.4 = 0.2 whereas P(G|R₁<R₃<R₂) =0.2*0.6 = 0.12

If it were R₃<R₁<R₂, we would classify the rock as granite as P(G|R₃<R₁<R₂) = 0.1*0.6 = 0.06 whereas P(B|R₃<R₁<R₂) = 0.05*0.4 = 0.02

(c)

Case 1: R₁<R₂<R₃:P(error) = 0.58*0.4 = 0.232

Case 2: R₁<R₃<R₂: P(error) = 0.8*0.6 = 0.48

Case 3: R₃<R₁<R₂:P(error) = 0.94*0.4 = 0.376

(d) Follow the same procedure as in (a) and (b). If we get a p where P(G)=0, then that p is the one where we will never classify the rock as granite.