Geometric and negative binomial

Applied Statistics and Probability for Engineers-Multiplication and Total Probability Rules-Part 3 [Answered]

4. Suppose 1% of cotton fabric rolls and 2% of nylon fabric rolls contains flaws. Of the rolls used by a manufacturer, 70% are cotton and 30%  are nylon. What is the probability that a randomly selected roll used by the manufacturer contains flaw?

5. 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 6%  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 efge roughness?

6. Computer keyboard failures are due to faulty electrical connects 12%  or mechanical defects 88%. Mechanical defects are related to loose keys 27% or improper assembly 73%. Electrical connect defects are caused by defective wire 35%, improper connection 13% or poorly welded wire 52%.

a) Find the probability that a failure is due to loose key.

b) Find the probability that a failure is due to improperly connected or poorly welded wires.