Can someone break down joint, conditional, and marginal probability with a finance example?

Let's build all these concepts using one consistent finance example. Consider a universe of 200 stocks:

Marginal (Unconditional) Probability:

The probability of an event without any conditions.

• P(L) = 100/200 = 0.50 (probability a random stock is large cap)
• P(E) = 110/200 = 0.55 (probability a random stock has positive earnings)

Joint Probability:

The probability of two events occurring together.

• P(L and E) = 70/200 = 0.35 (probability a stock is both large cap AND has positive earnings)

Conditional Probability:

The probability of one event given that another has occurred.

• P(E | L) = P(L and E) / P(L) = 0.35 / 0.50 = 0.70
• Given that a stock is large cap, there's a 70% chance it has positive earnings.

The Multiplication Rule:

P(A and B) = P(A | B) x P(B)

Verification: P(E | L) x P(L) = 0.70 x 0.50 = 0.35 = P(L and E) ✓

The Addition Rule:

P(A or B) = P(A) + P(B) - P(A and B)

P(L or E) = 0.50 + 0.55 - 0.35 = 0.70

70% of stocks are either large cap or have positive earnings (or both).

Independence Test:

Two events are independent if P(A | B) = P(A). Here, P(E | L) = 0.70 ≠ P(E) = 0.55, so being large cap and having positive earnings are NOT independent. Large caps are more likely to have positive earnings.

Exam tip: Build a joint probability table first (like above), then extract whatever probability the question asks for. This approach works for virtually every CFA Level I probability question.

Practice probability problems in our CFA Level I question bank.