Question

Conditional probability using two-way tables?

Please help me with the following question:

Answer 1

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`."