Okay kiddo, so you know when you get to choose what to wear or what toy to play with? That's called having free choice. In the same way, scientists use math to figure out if different things have something in common or if they're different. This is called making an inference.
Now, imagine you have a bunch of toys and some are in boxes with different colors. Let's say you pick a toy from a red box and then pick another toy from a blue box. Scientists use free choice inference to figure out if you picked the toys at random or if there is a reason why you picked those specific toys.
They do this by looking at the things you picked and seeing if they have something in common, like maybe they're both cars or they're both red. If they find something in common, then they can make an inference that you didn't pick the toys at random, but because of that common thing.
So basically, free choice inference is a way for scientists to figure out if there's a reason behind the choices we make, rather than just picking things randomly.