The edge roughness of slit paper products increases as knife

The edge roughness of slit paper products increases as knife blades wear. Only 2% of products slit with new blades have rough edges, 3% of products slit with blades of average sharpness exhibit roughness, and 4% of products slit with worn blades exhibit roughness. If 25% of the blades in the manufacturing are new, 60% are of average sharpness, and 15% are worn, what is the proportion of products that exhibit edge roughness? Round your answer to four decimal places (e.g. 98.7654).

Solution

Let

R = rough
N = new
A = average
W = worn

Then

P(R) = P(N) P(R|N) + P(A) P(R|A) + P(W) P(R|W)

= 0.25*0.02 + 0.60*0.03 + 0.15*0.04

= 0.0290 [ANSWER]