The Smith Floor Wax Company manufactures and sells industrial-strength floor wax in the wholesale market for home care products. The factory produces \(10,000 \mathrm{gal}\) of floor wax daily and currently has an inventory of 5,000 gal of floor wax in its warehouse. If sales of floor wax exceed production, the company meets the excess demand by using inventory; while if sales are less than production, the company adds this excess production to inventory. The company economist provides you with the following information concerning probabilities of daily sales events, where events are measured in gallons of wax sold.

\(A=[0,5,000], P(A)=.25\)

\(B=(5,000,10,000], P(B)=.65\)

C \(=[2,500,7,500], P(C)=.35\)
\(D=(5,000,7,500], P(D)=.20\)

a. What is the probability that inventory will have to be used to satisfy sales on a given day?

b. What is the probability that fewer than 2,500 gal of wax will be sold on a given day?

c. What is the probability of the event \(E=[0,2,500) \cup\) \((7,500,10,000]\) ?