Newly designed shipping containers for ampules were compared to the existing one to determine if…

Newly designed shipping containers for ampules were compared to the existing one to determine if the number of broken units could be reduced. One hundred shipping containers of each design (old and new) were subjected to identical rigorous abuse. The containers were evaluated and failures were defined as containers with more than 1% of the ampules broken. A total of 15 failures were observed and 12 of those failures were with the old container. If one container was selected at random:

a. What is the probability that the container will be of the new design?

b. What is the probability that the container will be a “failure”?

c. What is the probability that the container will be a “success”?

d. What is the probability that the container will be both an old container design and a “failure”?

e. What is the probability that the container will be either of the old design or a “failure”?

f. If one container is selected at random from only the new containers, what is the probability that the container will be a “failure”?

g. If one container is selected at random from only the old container design, what is the probability that the container will be a “success”?

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