Tuesday, November 11, 2008

Random-ness? Predicting the future

If I roll a dice, I have equal chances of getting a '6' or a '4'. However, if I have rolled a '6' once, then my second roll has lower chances of getting a '6'.

This is 'cause probability of getting two sixes in a row are low. However, both my rolls were independent rolls. Independently, I should have equal chances of a '6' both times. Then why does this happen?

Also, if 6 different people were to roll six different dice at the same time, theoretically we should get each of the numbers. But that isn't so in reality. Why?

Also, if V were to roll a six and then I were to roll, m probability of a 6 is low.

Can we predict the dice roll on the basis of previous rolls?

Now, let's make it simpler and take a coin; say I will be tossing the coin 3 times and I will have to predict the third toss result. First toss is 50-50 chance and I get a head. Second time , I get a head again. My prediction would then be a tail for the third one. BUT, what if I get a head and then a tail? What should my third guess be then? I would say head because the probability of two tails in a row is low. (But then again, head-tail-head should also be low. )

If I were to know what everyone on earth rolled till date and the number of times a number has been rolled, should I be able to predict the next number?

Going back to the original predict the future question, I don't think we can predict our own future just on probability alone. Example: pick a number between 1-20. Apparently, the most common human-generated-one is this.