3 ms·
You're making assumptions when you say that "the probability that you will CHOOSE TO LIFT the box containing the marble is 0.5". Consider that there may be 3 b
by tallanvor 14y ago
You're making assumptions when you say that "the probability that you will CHOOSE TO LIFT the box containing the marble is 0.5".
Consider that there may be 3 boxes, and the person setting up the experiment flipped a coin for each box. If the coin landed heads up, a marble was placed in the box. If the coin landed tails up, no marble was placed. This means there may be 0 - 3 marbles total. Until you know the actual state of the box, the probability remains 0.5.
- kstenerud 14y agoProbability is temporal. You need to specify timeframe. If you are talking about before the coins were flipped to decide whether a marble was to be placed into the box, then at that time BEFORE the coin was flipped, the probability would be 0.5 per box. If you are talking about AFTER the coin has been flipped, the probability for each box goes to either 0 or 1. This is regardless of whether an outside observer is aware of the state or not. If you were to now enter the room, having no knowledge of what boxes (if any) have had a marble placed in them, the probability of a marble being in a particular box has not changed. It is STILL either 1 or 0. There are only two ways to induce probability at this point: Pick a single, random box to open, in which case you are measuring the probability that you will choose a box with a marble in it (you are measuring yourself, not the marbles). The other is to guess whether a particular box has a marble in it, and then open it, in which case you are measuring whether your guess is correct or not (once again, measuring yourself, not the marble). Most people go wrong here because they think they are measuring one thing but are actually measuring something else.