The law of total probability is a rule relating marginal probabilities to conditional probabilities. It expresses the total probability of an outcome which can be realized via several distinct events.

Consider *n* mutually exclusive and collectively exhaustive events, *A _{1},
A_{2} … A_{n}*, the probability for any event

Taking cards for example (Exhibit 33.4), the probability of picking a queen:

$$P(Q)=P(Q│H)P(H)+P(Q│D)P(D)+P(Q|C)P(C)+P(Q|S)P(S)$$Basically, this is the same as weighted average.

*Example:* As shown is Exhibit 33.5, the age profile of a target population
(universe) is broken down into 4 groups: below 20, 20 to 30, 30 to 50 and over 50. The proportion of the
population that falls in each group is 20%, 20%, 40% and 20% respectively, and the proportion of brand
buyers in each is 10%, 15%, 20% and 15%. Based on this information, the proportion of brand buyers in the
target population is 16%, as computed in Exhibit 33.5.

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