AlmightySnoo , 9 months ago

Probability theory to the rescue:

Assume you have two binary variables X and Y. X is equal to 1 if you’re sick, 0 otherwise. Y is equal to 1 if you win the lottery, 0 otherwise.

Your question implicitly asks what the probability of winning would be given that you’re not sick. By definition that would be:

p = P(“X=0” and “Y=1”) / P(“X=0”)

And you’re stuck with the “X=0” and “Y=1” event as you need some knowledge about how X and Y are related to each other.

In other words, does your health have any effect on how the lottery machine works? Or vice versa, does the lottery machine impact your health? As the answer to both is obviously no (as there’s no physically possible way that could be true, unless you believe in the paranormal and there being some god who plays around with the probabilities), it’s reasonable to assume that X and Y are independent, in which case P(“X=0” and “Y=1”) = P(“X=0”) * P(“Y=1”), but then this simply means that p = P(“Y=1”), ie your health doesn’t matter: whether you’re healthy or sick, that doesn’t change the probability of you winning the lottery.