One method used 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 R3 denote measured spectrum intensities at three different wavelengths: typically, for granite R1, whereas for basalt R3. When measurements are made remotely (using aircraft), various orderings of the Ri's may arise whether the rock is basalt or granite. Flights over regions of known composition have yielded the following information (e.g., P(R1

	Granite	Basalt
R1	60%	10%
R1	25%	20%
R3	15%	70%

Suppose that for a randomly selected rock in a certain region, P(granite)=0.25 and P(basalt)=0.75.

1. Calculate P(granite|R1
2. If measurements yielded R1 < R3 < R2, how would you classify the rock? Answer the same question for R3 < R1 < R2.
3. Using the classification rules indicated in parts (a) and (b), when selecting a rock from this region, what is the probability of an erroneous classification?
4. If P(granite) = p rather than 0.25, are there values of p (other than 1) for which one would always classify a rock as granite?