$1)$ Jarir Bookstore is assessing whether to work with one or two Chinese suppliers. These suppliers are located on the East coast of China, which is susceptible to hurricanes. The company estimates that the probability of being hit by a hurricane that shuts down all suppliers for at least $2$ months is $5\%.$ It is also estimated that such a shutdown would cost the company $$100,000.$ On the other hand, the probability of only one supplier being shut down is $10\%.$ The cost of a shutdown for only one supplier will cost $$25,000$ for each month. Finally, the company estimates that the marginal cost of managing additional suppliers is $$12,000$ per year.Based on the above, please respond to the following questions:a$)$ Estimate the probability of experiencing a disruption with only one supplier.