# Defining target for Supervised learning classification

I would like to know if there is a way to predict an outcome (successful/failed or $$1/0$$) with and without a binary variable and compare their predict probability.

I have several variables. However, I consider only one of them: it is a binary variable indicating $$X=\left\{\array{1 & \textrm{if proposition was made}\\0 & \textrm{otherwise}}\right.$$ The outcome $$Y$$ is whether the contract was successful, i.e. $$Y=\left\{\array{1 & \textrm{if contract successful}\\0 & \textrm{otherwise}}\right.$$

What I want is actually to know in the future if I should propose or not the supplement, i.e. whether to set $$X=1$$ or rather $$X=0$$. Because sometimes when it is proposed ($$X=1$$) the contract is not successful ($$Y=0$$).

Quite basic approach is to calculate the probability of success for both possibilities $$P(Y=1|X=0) = \frac{N_{X=0 \land Y=1}}{N_{X=0}}$$
$$P(Y=1|X=1) = \frac{N_{X=1 \land Y=1}}{N_{X=1}}$$
where $$N_{\textrm{statement}}$$ stands for number of records where statement was true.
After this, you can pick $$X=0$$ or $$X=1$$ for which the probability is higher.
• $P(Y=0|X=1)=1-P(Y=1|X=1)$ Does it help? Oct 31 '18 at 18:17