# Resolved: The Law of total probability

in example: why not P(vegetarian | female) = 15/44???

The answer given in the video lecture is 15/47.

similarly, why not P(vegetarian | male) = 29 /44 ???

answer given in the video lecture was 29 /53

Hey Muhammad,

It's all in the conditional probability formula. First off, if we denote: A = vegeterian & B = female, then surely one can

easily see (with the table you provided) that:

P(A | B) = P(AB) / P(B) = 15 / (15 + 32) = 15/47 && P(B | A) = P(BA) ./ P(A) = 15 / (15 + 29) = 15/44.

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Following exactly the same logic and with the help of the table:

P(vegetarian | female) = P(vegetarian AND female) / P(female) = 15 / 47, because 47 is the total number of females

P(vegetarian | male) = P(vegetarian AND male) / P(male) = 29 / 53, because 53 is the total number of males

Hope that's all clarified now!

A., The 365 Team