The probability of understanding probability
OP - May 13, 2012, 05:07 AM
the first half of this is a boring explanation of basic probabilities, and most likely, pointless reading.
Consider two playing cards. For example; the ace of diamonds, and the 7 of clubs.
If you shuffle these two cards, and then look at the first card, there are two possibilities, each with equal probability. Either the first card can be the ace of diamonds, or it can be the 7 of clubs.
Let us say that the first card turns out to be the ace of diamonds. This is an event with a probability of 0.5, or 1 in 2.
If we add a third card and repeat the experiment, we now have two events to consider and multiply together.
1. The probability of the first card
2. The probability of the second card
Since there are three cards to choose from, event number one had a probability of 0.3333, or 1 in 3. Since there are two cards to choose from, event number two had a probability of 0.5, or 1 in 2.
The probability that these cards ended up in this order was 0.333 multiplied by 0.5, which is 0.1666, or 1 in 6.
If we continue this with experiment with an entire pack of (52) cards, whatever it is, the first card has a probability of 1 in 52, and the second has a probability of 1 in 51, etc etc etc .
In other words, the probability for a pack of cards to end up in any one order is 1 in (52 x 51 x 50 x 49 x 48 x 47 ..........x 3 x2 x 1), or 52 factorial.
When you shuffle a pack of cards, the probability that it ended up in that order was: One chance in 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000
If you do this experiment twice, you have now just witnessed an event with a probability of one chance in a number greater than the number of atoms in the universe.
It is often claimed by idiots that such events are impossible, but as you can see for yourself, not only are they possible, they happen all day, every day. If such an idiot were to be consistent with their logic, then they would be forced to conclude that every time a pack of cards is shuffled, a miracle happens, because it is so unlikely that this event could happen ‘just by chance’.
The mistake that idiots make is in assigning significance to an event that has already happened. Probabilities are useful for future events. Events that have already happened have a probability of 1 in 1, no matter how unlikely they were beforehand.
If you were to predict the order of the pack of cards before it had been shuffled, that would be an extremely impressive feat. However, to simply work out the odds of it happening in retrospect is utterly meaningless.
If a person believes that probabilities determined in retrospect prove that life needs a designer, or that the universe is too fine tuned to occur naturally, then the probability that this person understands probabilities is extremely low indeed. The arguments they propose are examples of the Texas Sharpshooter fallacy, in which you draw the target around the bullet hole after it has been fired.
Topic: The probability of understanding probability