Bloom$$s Jeans is searching for new suppliers, and Debbie Bloom, the owner, has narrowed her choices to two sets. Debbie is very concerned about supply disruptions, so she has chosen to use three suppliers no matter what.

$$ For option $1,$ the suppliers are well established and located in the same country. Debbie calculates the $$unique event$$ risk for each of them to be $4\%.$ She estimates the probability of a nationwide event that would knock out all three suppliers to be $2\mathrm{.}5\%.$

$$ For option $2,$ the suppliers are newer but located in three different countries. Debbie calculates the $$unique event$$ risk for each of them to be $20\%.$ She estimates the $$super$-$event$$ probability that would knock out all three of these suppliers to be $0\mathrm{.}4\%.$ Purchasing and transportation costs would be $$1,000,000$ per year using option $1$ and $$1,010,000$ per year using option $2.$ A total disruption would create an annualized loss of $$500,000.$

a$)$ What is the probability that all three suppliers will be disrupted using option $1?$

b$)$ What is the probability that all three suppliers will be disrupted using option $2?$

c$)$ What is the total annual purchasing and transportation cost plus expected annualized disruption cost for option $1?$

d$)$ What is the total annual purchasing and transportation cost plus expected annualized disruption cost for option $2?$

e$)$ Which option seems best?