Defining target for Supervised learning classification

Question

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 ($Y=0$).

Answer 1

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.