$1.$ In a manufacturing facility, materials are received by truck on Mondays. If materials stock out then special trips must be scheduled and these special trips are very costly$.$ We want to determine the likelihood of having to make a special trip for material for an assembly that has $6$ components and each component in the assembly has the same probability p of not stocking out during the week. $$

a$.$ To create an assembly, all six items must be in stock. What is the smallest that p can be for the components in this assembly so that the probability of having no stockouts for any of the six components during a delivery week $($and thus, you can make an assembly$)$ is less than $1\%?$

If each of the $6$ components in the assembly has a likelihood of stocking out during a delivery week of $1\mathrm{.}5\%($so p $=\mathrm{.}015),$ what is the likelihood that $2$ or more components stock out during the same week?