Suppose two companies, Company 1 and Company 2, are manufacturing a vaccine to treat COVID-19. Each company ships out 100 vaccines per shipment. A hospital is receiving40% of their vaccine shipments...

Suppose two companies, Company 1 and Company 2, are manufacturing a vaccine to treat COVID-19. Each company ships out 100 vaccines per shipment. A hospital is receiving40% of their vaccine shipments from Company 1 and the remainder of its vaccine shipments from Company 2. It is reported that from Company 1’s shipments, 7% of the vaccines gets damaged in shipping meanwhile from Company 2’s shipments, 3% of the vaccines gets damaged in shipping. Suppose the hospital recently received a shipment of 100 vaccines but we are not sure if this shipment came from Company 1 or Company 2. Assuming that the vaccines are independent of each other, what is the probability that exactly six vaccines in the shipment of100 are damaged? (If needed round to four decimal places).