A. A furniture manufacturer produces sofas. To improve their production process, they make a study of the sources of defects in the sofas. They find that 4% of the sofas have defects in the fabric but not the frame 1% of the sofas have defects in the frame but not the fabric 0.4% of the sofas have defects in both the fabric and the frame
a) construct a contingency table for this information.
b) What proportion of the sofas have defects in the fabric?
c) What proportion of the sofas have defects in the frame?
d) What proportion of the sofas have some type of defect (in either the fabric or the frame)?
e) Is having a defect in the fabric independent of having a defect in the frame? Show your reasoning.
f) Among sofas having a defect in the fabric, what is the probability of having a defect in the frame?
g) Knowing that a sofa does not have a defect in the frame, what is the probability it will not have a defect in the fabric? Show all work!