Acme typically produces three engines per day. Some of the engines pass the quality control inspection on the first try and are ready to be shipped; others need to be retooled. The probability of an engine needing further work is 0.05. If the engine is ready to be shipped, the company makes a profit of $10,000. If it needs to be retooled, it ultimately costs the company $2000. 

(a) Find the pmf of the number of engines that are ready to be shipped. 

(b) Find the pmf of the company's daily profit for the plant. 

(c) Find the expected profit.