Free lesson · Prediction foundations

Conditional probabilities and contract dependence

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A conditional probability asks how likely one event is inside the worlds where another event occurs. It is not generally the same as the unconditional probability.

Draw four states: both A and B, A only, B only, neither. The joint event occupies the overlap. A contract on A conditional on B needs explicit treatment when B does not occur; it may refund or settle using a special rule.

The product of marginal probabilities gives the joint only under independence. Shared candidates, economic releases or tournament structure often create dependence.

Apply it in a strategy

• Audit related-event contracts and build joint scenarios before combining exposures.
• Record the input timestamp, executable quantity, currency and horizon. Reconcile the result with a cash-flow or state table.
• Stress this failure condition: Textually similar events may use incompatible dates or rules, and independence cannot be inferred from separate listings.

Research deliverable

Build and explain a conditional probabilities and contract dependence worksheet. Audit related-event contracts and build joint scenarios before combining exposures.

Evidence boundary: Synthetic arithmetic and scenarios illustrate mechanics. They are not historical returns, a paper replication, or evidence of an executable edge. Research sources and their access limitations are recorded at the end of this module.

# Python 3.10+; standard library unless NumPy is imported below.
# Inputs and outputs use the units defined in this lesson. Synthetic teaching example.
def conditional(joint,conditioning):
    if not 0<conditioning<=1 or not 0<=joint<=conditioning: raise ValueError("Invalid joint mass")
    return joint/conditioning

print(conditional(.30,.40))