If two components each have a failure probability of 0.1 and operate in parallel, what is the probability the system fails?

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Multiple Choice

If two components each have a failure probability of 0.1 and operate in parallel, what is the probability the system fails?

Explanation:
In a parallel setup, the system fails only if every path fails. Here, each component has a 0.1 chance of failing, and their failures are independent. The chance both fail is 0.1 × 0.1 = 0.01, so the system failure probability is 0.01 (1%). The system’s reliability in parallel is then 0.99, since at least one component would succeed. If the failures weren’t independent, we’d need the joint probability to compute the result.

In a parallel setup, the system fails only if every path fails. Here, each component has a 0.1 chance of failing, and their failures are independent. The chance both fail is 0.1 × 0.1 = 0.01, so the system failure probability is 0.01 (1%). The system’s reliability in parallel is then 0.99, since at least one component would succeed. If the failures weren’t independent, we’d need the joint probability to compute the result.

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