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 receiving 40% 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 of 100 are damaged?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...
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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 receiving
40% 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 of
100 are damaged?

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