# Problem Management — principlesProbability

Probability is the misapplication of statistics to inappropriately small samples.

Probability is simply a mathematical tool that is used in statistics. Probability by itself is almost useless in reality (where reality perhaps doesn't include the world of quantum physics).

Consider the following situation. Six people are sitting at a round table. I go to the vacant 7th seat, take something out of my pocket, shake it, slam it on the table, and tell everyone that there are two quarters under my hand.

The person to my right, R1, was fast enough to see a tail. He lyingly whispers to R2, I saw that one of them was a head. On my left, L1, who saw that the coin closest to him was a head that couldn't possibly have been seen by R1, overhears this. L2 saw that the coin closest to L1 was a head. L3, being a numismatist, knows that the new commemorative quarters are slightly heaver on the head side. R3 saw and heard nothing.

What would each person say is the probability that the coins are both heads-up?

 L3 — 23%There's a slight tendency for heads to be down R3 — 25%It must be one of HH, HT, TH, or TT L2 — 50%The second coin could be heads or tails R2 — 33%One's a head, so only HH, HT, and TH are possible L1 — 100%My side was a head, and R1 says his was too ME — 0% or 100%It's exactly 0% or 100%, but I've no idea which R1 — 0%One's a tail, so the other doesn't matter

Only R1 is correct and certain, but can any of the others be said to be wrong? Does probability (as opposed to statistics) have anything at all to say about reality? Or is it simply a measure of our own inadequate knowledge?