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FRM Part II · FRM Exam Part II · Guidance on Managing Outsourcing Risk

A bank uses 10 critical services, each hosted by one of two cloud providers. Provider X hosts 6 services and Provider Y hosts 4. Each provider independently has a 2% probability of a severe multi-day outage in a year. Assuming independence, what is the probability that at least one critical-service outage occurs and, separately, that both providers fail, respectively (rounded)?

The probability of at least one provider failing is 1 minus 0.98 squared, which is 3.96%. The probability that both fail is 0.02 times 0.02, or 0.04%. Simply adding the probabilities overstates the first figure because it double counts the joint case.

  1. A3.96% and 0.04%Correct
  2. B4.00% and 0.04%
  3. C3.96% and 0.40%
  4. D2.00% and 0.04%

Explanation

At least one failure = 1 − 0.98 × 0.98 = 1 − 0.9604 = 3.96%. Both fail = 0.02 × 0.02 = 0.04%. Simply adding 2% + 2% ignores the overlap and gives 4.00%. A 0.40% joint figure wrongly multiplies by 10 services.

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