In the manufacturing of a chemical adhesive, 3% of all batches have raw materials from two different lots. this occurs when holding tanks are replenished and the remaining portion of a lot is insufficient to fill the tanks. only 5% of batches with material from a single lot require reprocessing. however, the viscosity of batches consisting of two or more lots of material is more difficult to control, and 40% of such batches require additional processing to achieve the required viscosity. let a denote the event that a batch is formed from two different lots, and let b denote the event that a lot requires additional processing. determine the following probabilities:
a. p(a)
b. p(a')
c. p(b\a)
d. p(b\a')
e. p(a ∩ b)
f. p(a ∩ b')
g. p(b)