$$Bloom$\text{'}$s Jeans is searching for new$$ 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$$ "unique$-$event" risk for each of them to be $3\%.$ She estimates the probability of a nationwide event that would knock out all three suppliers to be $2\mathrm{.}7\%.$ For option$2,$ the suppliers are newer but located in three different countries. Debbie calculates the$$ "unique$-$event" risk for each of them to be $21\%.$ She estimates the$$ "super$-$event" probability that would knock out all three of these suppliers to be $0\mathrm{.}5\%.$ Purchasing and transportation costs would be $$$$1,200,000$ per year using option $1$ and $$$$1,210,000$ per year using option $2.$ A total disruption would create an annualized loss of $$$$550,000.$

Part $2$

$$a$)$ The probability that all three suppliers will be disrupted using option $2$ is