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?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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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