According to Section 11.2.1 of API 580:
"The probability of credible events leading up to the specific consequence should be factored into the probability of the specific consequence occurring." Additionally:
"It is important to understand this linkage between the POF and the probability of possible resulting incidents... The probability of a specific consequence is tied to the severity of the consequence and may differ considerably from the probability of the equipment failure itself." Option A is correct and emphasized directly in API 580.
Option B is incorrect because considering all credible events is essential.
Option C is incorrect: the probability of a consequence typically decreases with severity.
Option D is incorrect: the probability of consequence is linked to the probability of failure.
Reference: API 580, 2nd Edition (2016), Section 11.2.1 - Determination of the Probability of a Specific Consequence

API 580, Section 12.4 and 12.6 emphasize that inspection should be optimized and risk-focused. Excessive inspections can increase exposure to damage mechanisms (such as mechanical or corrosion risks introduced during inspection activities), especially if not needed.
From Section 12.4:
"Organizations should be deliberate and systematic in assigning the level of risk management achieved through inspection and should be cautious not to assume that there is an unending capacity for risk management through inspection." Further, in risk-optimization contexts (Section 12.5):
"While there is a potential for reduction of inspection costs through utilization of RBI, increased equipment integrity and inspection cost optimization should remain the focus." Therefore, excess inspections may be:
Unjustified
Economically wasteful
Risk-enhancing (e.g., opening equipment unnecessarily may lead to deterioration) Reference: API 580, 2nd Edition (2016), Sections 12.4 and 12.6

As per API 580, failure is typically defined in terms of a breach in the pressure boundary - most clearly indicated by loss of containment. In Section 5.2, API 580 explains the fundamental focus of RBI:
"One objective of RBI is to determine what incident could occur (consequence) in the event of an equipment failure and how likely (probability) it is that the incident could happen. For example, if a pressure vessel subject to damage from corrosion under insulation develops a leak, a variety of consequences could occur." This leak constitutes a loss of containment and is therefore categorized as a failure.
Other options are not necessarily defined as equipment failures:
B (corrosion beyond allowance) is degradation, but failure only occurs if it breaches containment.
C (end of service life) is a lifecycle condition, not a failure by definition.
D (fire or explosion) are consequences of a failure, not the failure itself.
Reference: API 580, 2nd Edition (2016), Section 5.2

API 580 defines risk mitigation as follows:
"Risk mitigation: Process of selection and implementation of measures to modify risk. The term risk mitigation is sometimes used for measures themselves." This definition is provided in Section 3.1.67 of API 580. It is also emphasized throughout the document that mitigation may address either probability or consequence or both, and includes actions such as inspection, maintenance, repair, replacement, and design changes.
Reference: API 580, 2nd Edition (2016), Section 3.1.67
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According to Section 5.3.6:
"The spectrum of risk analysis should be considered to be a continuum with qualitative and quantitative approaches being the two extremes of the continuum and everything in between being a semi-quantitative approach." This clearly defines the "continuum" as ranging from qualitative to quantitative methods, with semi- quantitative approaches in between.
Reference: API 580, 2nd Edition (2016), Section 5.3.6