Thank you for the correction, here is the proof using LaTeX:

Let $x$ and $y$ be two random integers. The product $xy$ is odd if and only if both $x$ and $y$ are odd.

The probability that $x$ is even is $\frac{1}{2}$ and the probability that $x$ is odd is also $\frac{1}{2}$. By the same reasoning, the probability that $y$ is even is $\frac{1}{2}$ and the probability that $y$ is odd is $\frac{1}{2}$.

The probability that the product of $xy$ is odd is:

$\frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}$

The probability that the product of $xy$ is even is :

$1 - \frac{1}{4} = \frac{3}{4}$

Thus, the probability that $xy$ is even is $\frac{3}{4}$.
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