I need some help in resolving a dispute. Recently, a friend of mine told me that the probability of rolling a 6 on the second roll of a die after not rolling a 6 is not 1/6. He believes it is not 1/6 but rather the probability of rolling 6 after not rolling a 6 increases with each subsequent roll.
However, this seems really silly to me.
Shouldn't the probability of getting a 6 on the second role after not getting a six on the first role be 6/6 x 1/6? By using the 6/6, I'm just signifying that there is no probability the first role was a 6 since we've already rolled it and it WASN'T A SIX!
In our argument, I proposed this thought experiment. I roll one die behind a curtain and can't see which number is rolled. I then roll the second die in front of the curtain and can observe what number comes up. Now, the probability of the second die coming up with a 6 is 1/6, no? The outcome of the first die will have no effect on the second die. We argued about that one for an hour. . .
Thanks for the help.