Mathematics, 25.10.2019 01:43 hannahsambrano12

The edge roughness of a slit paper products increases as knife blades wear. only 1% of products slit with new blades have rough edges, 3% of products shot with blades of average sharpness exhibit roughness, and 5% of the 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 blades.

a. what is the proportion of products that exhibit edge roughness?

b. if a paper was selected at random and found that it has rough edges, what is the probability that it was slit by a new knife blades?

c. if a paper was selected at random and found that it has rough edges, what is the probability that it was slit with a blade of average sharpness blades or worn blades?

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Answer from: deena7

a) 2.8% of products exhibit edge roughness.

b) If a paper has rough edges, there is an 8.93% probability that it was slit by a new knife blades.

c) If it has rough edges, there is a 91.07% probability that it was slit with a blade of average sharpness blades or worn blades.

Step-by-step explanation:

We have these following probabilities:

A 25% probability that the blade is new

A 60% probability that the blade is of average sharpness.

A 15% probability that the blade is worn.

If a blade is new, a 1% probability that it has rough edges.

If a blade is of average sharpness, a 3% probability it has rough edges.

If a blade is worn, a 5% probability it has rough edges.

a. What is the proportion of products that exhibit edge roughness?

This is

$P = P_{1} + P_{2} + P_{3}$

$P_{1}$ are those that are new and exhibit edge roughness. So $P_{1} = 0.25*0.01 = 0.0025$

$P_{2}$ are those of average sharpness that exhibit rough edges. So $P_{2} = 0.6*0.03 = 0.018$

$P_{3}$ are those that are worn and exhibit rough edges. So $P_{3} = 0.15*0.05 = 0.0075$

$P = P_{1} + P_{2} + P_{3} = 0.0025 + 0.018 + 0.0075 = 0.028$

2.8% of products exhibit edge roughness.

b. If a paper was selected at random and found that it has rough edges, what is the probability that it was slit by a new knife blades?

From a), we found that there is a 0.028 probability that it has rough edges.

Also, there is a 0.0025 probability that it was slit by a new knife blades and have rough edges. So

$P = \frac{0.0025}{0.028} = 0.0893$

If a paper has rough edges, there is an 8.93% probability that it was slit by a new knife blades.

c) If a paper was selected at random and found that it has rough edges, what is the probability that it was slit with a blade of average sharpness blades or worn blades

From a), we found that there is a 0.028 probability that it has rough edges.

Also, there is a 0.018 probability that it was sliced with a blade of average sharpness and has rough edges and an 0.0075 probability that it was slices with worn blades and has rough edges. So

$P = \frac{0.018 + 0.0075}{0.028} = 0.9107$

If it has rough edges, there is a 91.07% probability that it was slit with a blade of average sharpness blades or worn blades.

Answer from: Quest

gaddgad

step-by-step explanation:

Answer from: Quest

What's the denominator

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