Question

the edge roughness of slit paper products increases as knifeblades wear. only 1% of products slit with new blades have roughedges, 3% of products slit with blades of average sharpness exhibitroughness, and 5% of products slit with worn blades exhibitroughness. if 25% of the blades in manufacturing are new, 60%are average sharpness, and 15% are worn, what is the proportion ofproducts that exhibit edge roughness?

Answer 1

Answer: There is 2.8% of products that exhibit edge roughness.

Step-by-step explanation:

Let A₁ be the event that blades are new.

Let A₂ be the event that blades are average sharpness.

Let A₃ be the event that blades are worn.

P(A₁) = 25% = 0.25

P(A₂) = 60% = 0.60

P(A₃) = 15% = 0.15

Let the B be the event that selected blade is rough.

So, P(B|A₁) = 0.01

P(B|A₂) = 0.03

P(B|A₃) = 0.05

So, P(B) would be

$P(A_1)P(B|A_1)+P(A_2)P(B|A_2)+P(A_3)P(B|A_3)\\\\=0.25\times 0.01+0.60\times 0.03+0.15\times 0.05\\\\=0.028$

Hence, there is 2.8% of products that exhibit edge roughness.