Conditional probability using two-way tables?

Please help me with the following question:

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1 Answer
Dec 7, 2017

The question does not specify what value of X we want the probability of.

Explanation:

If we want the probability mass function of this scenario, we could say

"P"(X=x | Y=1)={color(white)(color(black)((4/7", "x=0),(3/7", "x=1),(0", "x=2))

This is because (2/9)/(2/9+1/6)=4/7 and (1/6)/(2/9+1/6)=3/7.

It only makes sense to talk about the probability of an event. In its current form, the question presumes X is an event. But X is a random variable, so an appropriate event would be when X takes on a specific value. For instance, we could easily ask for the probability that X is 0, given that Y is 1. (This answer would be 4/7.)

I suppose one could make a case for the correct answer being 7/18, since that's the sum of all the values in the row Y=1. But again, this assumes X is an event. Based on the information given, it is incorrect to say "the probability of X occurring given Y=1 is equal to 7/18."