Conditional probability using two-way tables?

Please help me with the following question:

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1 Answer
Geoff K.
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#."

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