Can you show a breakdown of how you solve this problem

ICU Corp. makes lenses for telescopes. One feature of a lens is its ability to focus light, also known as resolution. Each lens that ICU Corp. produces has a resolution specification that it must meet. Every lens leaving production goes through an automated focus resolution test. Lenses which pass the test are deemed acceptable and are shipped. Lenses that fail the test are deemed unacceptable and scrapped. The test, while inexpensive and very fast, is not perfect. Lenses that meet their required specifications fail the test 4% of the time and lenses that do not meet their required specifications pass 3% of the time. It is known that 5% of lenses leaving production do not meet their required specifications.

a)What is the probability that a randomly selected lens will fail the focus test?

b)What is the probability that a lens that fails the test does not meet its required specification?

c)What fraction of lenses which pass the test are actually do not meet their required specifications?

d)ReDo Optics Inc. has proprietary focus testing technology that allows it to identify a lens that meets specification with 100% accuracy and to identify a lens that does not meet specification with 100% accuracy. ReDo has offered to purchase ICU's lenses that do not pass the resolution test for $1 per lens. A lens that meets its required specification can be sold for $100, a lens that does not can be sold for scrap for $0.5. The cost of transportation and testing is $2 per lens. What is ReDo Optics' expected profit per failed lens that it buys?