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**ANDS!** I think you are confusing yourself with what the question is asking. Not to be blunt, but literally, you are being asked for the random variables whose values are odd (i.e. not even, not divisible by 2). If I asked you to toss a dice, and give me the probability of getting an ODD NUMBER, how would you go about that? This question is no different:

The probability of X being odd is P(X=1 or X=3).

The probability of the random variable XY being odd is P(XY=1, 3, 9).

The last one is a conditional. Do you know how to compute marginal probabilities? What is the probability of X being equal to 1 over ALL values of Y (since this is a joint pdf)? That is the probability of X being equal to 1. We call them "marginals", because you would (to make it less messy) scribble the total probabilities in the "margins" of your chart there. Once you compute the marginal, it is simple to compute P(Y|X is odd).