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I am currently working on a project, a sample start-up. Suppose I have these data:

$N$ = total population.

$n_1$ = number of mall shoppers.

$n_2$ = number of people aged from 18-65.

$n_3$ = number of people with smartphones.

The question is how do I get the number of mall shoppers who are aged 18-65 and also have smartphones from the total population of the country? This number would then result to the approximate target audience for my start-up project but I don't know how to get it.

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Let $A$, $B$, and $C$ be the sets of people in your population, such that $\vert A \cup B \cup C \vert = N$. If you treat these as proportions (i.e. A is the proportion of people in the population which shop at a mall) then you perhaps can use some laws of probability to find what you need.

You want to know $P(A \cap B \cap C)$ given that $P(A) = n_1/N$, $P(B) = n_2/N$, and $P(C) = n_3/N$. In order to do this, you will first need to know the size of the pairwise intersections (e.g. you need to know how Many people shop at a mall AND are between 18-65). Do you have that information?

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  • $\begingroup$ I don't have that information. I only have individual information of the sets of people. $\endgroup$
    – ddwy
    Commented Nov 12, 2018 at 16:12
  • $\begingroup$ I don't think you'll be able to get the size of the intersection without that information. $\endgroup$
    – Demetri Pananos
    Commented Nov 12, 2018 at 16:14
  • $\begingroup$ But suppose I have that information. I have 250,000 people who shop at a mall and are 18-65, what do i do next? $\endgroup$
    – ddwy
    Commented Nov 12, 2018 at 16:18
  • $\begingroup$ There is a formula for computing the probability of the intersection of three events. You would use that formula to compute the size of the intersection. Then, multiply by the size of the population to get the number of people who satisfy your criteria. $\endgroup$
    – Demetri Pananos
    Commented Nov 12, 2018 at 16:29

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