how to find probability of one or more events to happen from an incomplete data set I have a dataset that gives information of a population. For instance, I know the fraction of people that are males (M) and that are within a certain age range (A), P(M &amp; A), and then I know the fraction of males that live in a certain area (L), P(M &amp; L).

What I'm interested in computing is P(M &amp; A &amp; L), which is the fraction of people that are males, are within a certain age range and live in a certain area. 

Using Baye's formula I can say that

P(M &amp; A &amp; L) = P(M &amp; A | L) P(L)


But my dataset only gives P(L) and not P(M &amp; A | L). However, if I assumed that M &amp; A and L are independent I have

P(M &amp; A | L) = P(M &amp; A) P(L)


How large is the error on P(M &amp; A | L) if I make this assumption. Do you know of any other method I could use to estimate P(M &amp; A | L) without assuming independence?
Bayes Theorem applies to conditional probabilities. 
$
     P(A|B) = \frac{P(A).P(B|A)}{P(B)} 
    $

The question you have posed is one of multiple events occurring together. If the events can be considered to be independent of each other, then,

P(A &amp; B &amp; C) = P(A).P(B).P(C)


In your question above, 

P(M &amp; A &amp; L) = P(M &amp; A).P(L) = P(M).P(A).P(L)


Based on the data provided by you, you should have these probabilities or can derive them by appropriate summations.

Let's say that .1 probability of males are between 1-10 years of age. Further, probability of males in location L is 0.2. So the probability of males in 1-10 years of age in Location L is 0.1 X 0.2 = 0.02 . This is assuming that all locations have the same probability distribution of age ranges.