Fault tree gates (independent events)
Used on the ASP and CSP. The worked example below is computed by code and checked against the source.
OR gate: P = P(A) + P(B) − P(A)P(B)
AND gate: P = P(A) × P(B)
P = probability of each independent basic event.
Worked example
P(A) = 0.1, P(B) = 0.2.
OR: 0.1 + 0.2 − 0.02 = 0.28; AND: 0.1 × 0.2 = 0.02
Where it appears on the exam
ASP: ASP11 Domain 1, Mathematical Calculations
Blueprint: ASP11 Domain 1, task 12: probability of failure mode
Practice: Statistics and Probability, System Safety Analysis: Fault Trees and FMEA
CSP: CSP11 Domain 2, Program Management
Blueprint: CSP11 Domain 2, task 6: system safety analysis techniques (fault tree analysis)
Practice: Risk Matrix and Fault Tree Probability
Source
The formula comes from
NUREG-0492, Fault Tree Handbook (U.S. NRC, 1981), Chapter VII(opens nrc.gov in a new tab)“If A and B are independent events, then P(BIA) = P(B) and P(Q) = P(A) + P(B) - P(A) P(B); ... If A and B are independent events, then P(BIA) = P(B), P(AIB) = P(A), and P(Q) = P(A) P(B);”
Questions
- What is the formula for fault tree gates (independent events)?
- OR gate: P = P(A) + P(B) − P(A)P(B); AND gate: P = P(A) × P(B). P = probability of each independent basic event.
- Will this formula be given on the BCSP exam?
- BCSP says the formula is included in the question whenever one is needed, unless the question is testing whether you know the formula. You can't bring a formula sheet into the exam, so learn what each formula does and when to use it.
BCSP on formulas at the exam
BCSP, What to Expect When Sitting for a BCSP Exam (item 7)(opens bcsp.org in a new tab)“For any question requiring a mathematical formula, the formula will be included within the exam question (unless the question is specifically testing your knowledge of a formula). You will not be provided or permitted to bring a formula sheet.”
Related
- Risk (system safety)
- Fault tree analysis
- Mean, median and sample standard deviation
- Force from mass and deceleration
- Unit conversions
- ASP formula sheet
- CSP formula sheet
Checked 2026-10-16. Spot a problem? Email hello@passcited.com.