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 33.5), 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 33.6, 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 33.6.

MarketingMind’s content is sourced from the **Marketing Analytics Practitioner’s Guide (MAPG)**, a comprehensive 4-volume compendium on Marketing, Marketing Analytic and Market Research available in both physical and eGuide formats. (Click to learn more).

Previous Next

*Use the Search Bar to find content on MarketingMind.*

In an analytics-driven business environment, this analytics-centred consumer marketing workshop is tailored to the needs of consumer analysts, marketing researchers, brand managers, category managers and seasoned marketing and retailing professionals.

Unlock the Power of Digital Marketing: Join us for an immersive online experience designed to empower you with the skills and knowledge needed to excel in the dynamic world of digital marketing. In just three days, you will transform into a proficient digital marketer, equipped to craft and implement successful online strategies.