FRM: Probability

Explanations, applications and practice for probability.

• Mutually exclusive and independent events

  Use joint probabilities to distinguish non-overlap from independence, including the zero-probability edge case.

  Comparisons

• Conditional and joint probability: different denominators

  Distinguish the share of all outcomes from the share within a conditioning event.

  Concepts

• Prior, likelihood and posterior probability

  Identify the probability before evidence, the evidence model and the probability after conditioning.

  Concepts

• Random variables, outcomes and events

  Distinguish a model scenario, a numerical return mapping and an event set.

  Concepts

• Odds for, odds against and probability

  Identify the denominator and quotation direction before converting an odds ratio.

  Formulas

• Checking probabilities and a complete scenario partition

  Check individual bounds, overlaps and the sum across mutually exclusive exhaustive scenarios.

  Lessons

• Checking a two-stage probability tree

  Check each conditional split, path product and terminal probability.

  Lessons

• Why P(A given B) differs from P(B given A)

  Recover the joint probability, then divide by the probability of the new condition.

  Common mistakes

• Probability relationships practice

  Practise odds direction, positive-probability independence and conditional denominators.

  Practice
• 

  Bayes probability update calculator

  Combine a prior with evidence probabilities under an event and its complement.

  Tools
• 

  Odds and probability calculator

  Convert odds for a risk event into event and complement probabilities.

  Tools

• Updating a control-weakness probability after an exception flag

  Calculate both flag branches before interpreting the posterior.

  Worked examples

• Expected revenue from a two-stage scenario model

  Calculate conditional expectations, then apply the outer scenario probabilities.

  Worked examples

• Converting odds against default into a default probability

  Work through the event label, quotation direction and normalization.

  Worked examples

• Calculating the probability of at least one event

  Subtract the overlap once when adding two event probabilities.

  Worked examples

• Combining conditional probabilities with scenario weights

  Calculate an unconditional probability from a complete weighted scenario table.

  Worked examples