Calculate the probability that the gold component is neither sufficiently pure nor sufficiently conductive to be shipped. (ii)  Are the two events – of the gold component being sufficiently pure, and of the gold being sufficiently conductive – mutually exclusive or independent or neither? Explain your answer. (iii)  If a gold component is deemed to be sufficiently conductive to be shipped, what is the probability that it is sufficiently pure to be shipped?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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The quality of a manufactured gold component is assessed for both its purity and its conductivity
prior to being shipped. Investigations have shown that the probability that the gold component has
sufficient purity to be shipped is 90%, and the probability that the gold component has sufficient
conductivity to be shipped is 80%. The probability that the gold component is both sufficiently
pure and sufficiently conductive to be shipped is 75%.

(i)  Calculate the probability that the gold component is neither sufficiently pure nor
sufficiently conductive to be shipped.

(ii)  Are the two events – of the gold component being sufficiently pure, and of the gold
being sufficiently conductive – mutually exclusive or independent or neither? Explain your
answer.

(iii)  If a gold component is deemed to be sufficiently conductive to be shipped, what is
the probability that it is sufficiently pure to be shipped?

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