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enter image description here

I came to ask this question because I couldn't understand an answer in What are the differences between "Marginal Probability Distribution" and "Conditional Probability Distribution"?

In the answer, the chart above is shown, and the difference between marginal probability distribution and conditional probability distribution is explained.

While I understood the difference of the two, I suddenly got a bit confused about the calculation of conditional probabilities.

The answer in that post contained this: enter image description here

If P(X = x1) = 0.6, I would expect P(Y = y1) = 0.617.

And if joint probabilities is simply the product of two probabilities, P(X = x1, Y = y1) = P(X = x1)P(Y = y1), then doesn't that mean

P(Y = y1|X = x1) = 0.617, considering the P(X = x1)s will cancel out?

Sorry if this seems like a lazy question. I will definitely try to find out what's happening before an answer.

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The root of your mistake is in the sentence: "And if joint probabilities is simply the product of two probabilities" - This is only true for independent variables. This is not the case here.

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  • $\begingroup$ Thank you for the answer. However I am still a bit confused about how to calculate P(X|Y). If x and y are dependent variables, it would mean P(X|Y) = P(X,Y)/P(Y) = P(X|Y)(P(Y)/P(Y). Does this mean I would be able to solve this question only when P(X,Y) is a given..? (obviously this is something I should look up...) $\endgroup$
    – rivid
    Commented Apr 2, 2021 at 8:39
  • $\begingroup$ Nevermind I think I understood what it means. It seems like if you had more context in a given question, you can calculate P(X|Y) on other basis given from the question. $\endgroup$
    – rivid
    Commented Apr 2, 2021 at 8:52

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