Question

The edge roughness of slit paper products increases as knife blades wear. Only 1% of products slit with new blades have rough edges, 3% of products slit with blades of average sharpness exhibit roughness, and 5% of products slit with worn blades exhibit roughness. If 25% of the blades in manufacturing are new, 60% are of average sharpness, and 15% are worn, what is the proportion of products that exhibit edge roughness?

Answer 1

Answer: Our required probability is 2.8%.

Step-by-step explanation:

Since we have given that

Probability of products slit with new blades have rough edges P(X) = 1%

Probability of products slit with blades of average sharpness exhibit roughness P(Y) = 3%

Probability of products slit with worn blades exhibit roughness P(Z) = 5%

Let A be the  selected product that exhibit edge roughness.

P(A|X) = 25% = 0.25

P(A|Y) = 60% = 0.60

P(A|Z) = 15% = 0.15

So, the probability of products that exhibit edge roughness is given by

$P(X)P(A|X)+P(Y)P(A|Y)+P(Z)P(A|Z)\\\\=0.01\times 0.25+0.03\times 0.60+0.05\times 0.15\\\\=0.028\\\\=2.8\%$

Hence, our required probability is 2.8%.