Discussion
Two independent displays each fail at \( 10^{-4} \) per hour. The probability both fail in the same hour, assuming independence, is
Answer: D
Correct answer: \( 10^{-8} \)
For independent events the joint probability is the product:
\[ 10^{-4} \times 10^{-4} = 10^{-8} \]
The result is only as good as the independence assumption, which is the real lesson. Two displays sharing a symbol generator, a power supply, a cooling duct or a software load are not independent, and a common cause can defeat the calculation entirely. This is why redundancy is pursued through dissimilarity and segregation, not merely by fitting two of something.
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