# Mission improvement - Data Analyst/Python/Probability and Statistics/conditional probability: Intermediate

Hello,

I just want to suggest some improvements on the topic Formula for Three Dependent Events that could possibly aid in understandability of the topic.

We are supposed to formulate a multiplication rule that caters for three dependent events A, B, and C. I suggest the following;

Since we already know that the multiplication rule for two dependent events A, B is given by
P(A n B ) = P(A) * P(B|A) ------- (1)
For three events A, B, and C we have
P(A n B n C) = ?
let x = A n B ----- (2)
P(x n C) = P(x) * P(C | x) ------ (3)
substituting (2) in (3)
P(A n B n C) = P(A n B ) * P(C | A n B) ------ (4)
Simplify (4) by substituting (1) in (4)
P(A n B n C) = P(A) * P(B|A) * P(C | A n B)

I think this is much easier to follow approach especially if we were to extend the rule to 4 or more dependent events.

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Hello @markmanu21

Welcome to DQ Community I suggest you to address the concern here with the detail explanation…

Thanks for understanding

Best
K!

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