Like. I know they are different and that one is less likely. But could someone explain this in a way that I can explain it to my partner? I know it is true but cannot remember anything about why and how to explain my point.
In: 6
We often assume (usually pretty reasonably) that events are “Independent”. Probability only really works in the simple, easy-to-understand way that is taught in 300-level undergrad intrductory courses if you assume this. You roll a die, it doesn’t remember what just happened and change its next roll because of it- the die has no memory. It is, after all, an inanimate object.
If you roll six dice, each number has six different one in six chances to come up. But the dice can’t see each other! And even if they could, they can’t change their roll. Thus, if you roll six dice, it is possible not to get one of each number. Quite common, in fact.
Many repeated chances gives many possible outcomes. If you take 10 7% chances, it is possible (if quite unlikely) to hit the chance all 10 times- something that *cannot* happen with one 70% chance.
Possibly confusing the matter is “Expected Value”. With expected value, 10 7% chances are indeed the same as one 70% chance. This is because their outcomes are the same *in the long run*. 10 7% chances will sometimes turn out quite differently than one 70% chance, but one million 70% chances and ten million 7% chances will approximately always look very, very similar.
But life is lived in the small moments. Thus does probability occasionally make fools of us all.
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