Pairs of dice are tossed 10 times (10 experiments). We know that first dice rolled 4 times with some specific number (let's say number one) out of all 10 experiments. We know that the second dice rolled 2 times with the same number one. How to calculate probability of both 2 dice NOT rolling number one in any of this 10 experiments simultaneously?
from first dice perceptive there is
(10-2)/10 = 0.8 probability that second dice is not number one in the same experiment. And we know first dice rolled 4 times total. So that I'd calculate total probability as
0.8 ^ 4 = 0.4096.
However if you look from second dice perspective you will see that it's
(10-4)/10 = 0.6 chances first dice is not number one in the same single experiment. Then for 2 experiments where we have number one for second dice we'll get
0.6 ^ 2 = 0.36 outcome.
why do I get different results here? What is the right way to solve this task?