regnis, I tried giving an example to Alan so he could understand what conditional probability is. He ignored the examples. I'm hoping you won't ignore my following example:


Let's say I have 10 marbles on the table. 5 are red and 5 are blue. I tell you to pick a random marble (you can't see them). I ask you, what is the probability you picked a blue marble?

Hopefully, you would say 50%. Do you agree?


Now, let's say we do the exact same exercise. But this time, I remove a few of the blue marbles. You still can't see the marbles. I tell you to pick a random marble and I ask what's the probability/chance that you picked a blue marble? Would you still say you have a 50% chance to have picked a blue marble?

Or rather, let's make it seem dead obvious: I remove all the blue marbles except for 1. Then you pick one. Is the probability you picked a blue marble still 50%?



This is the same thing with the dice problem.

I roll two dice. Each die has a 1/6 chance of being a 2 (like a marble has a 1/2 chance of being blue). But then we essentially remove the die that is showing a 2 (in the same way that I removed a blue marble). For the remaining die, the chance of it showing a 2 has decreased from 1/6 (just like of the remaining marbles, you have less than a 50% chance of picking a blue marble).