I am taking intro stats. This is a practice problem from my book, and I am a little confused about whether to use conditional probability or if I am thinking about the problem incorrectly.
If we roll a fair die twice, what is the probability of the event ${\left(x,y\right)|x\neq y}$.
I know that P(x,y) = 1/6 * 1/6 = 1/36 since the two rolls are independent. I also see that there are 6 possibilities where x=y $\rightarrow$ (1,1), (2,2), ...(6,6).
Is this an instance where we use $P(x|y) = P(\frac{x \cap y}{y}$), since $x$ is dependent on $y$?
Or since the roll of the first die is independent (1/6), but then the roll of the second die is dependent on the roll of the first, and is given only 5 options in which it is not equal to the roll of the first (1/5)?
Thank you in advance for shedding any knowledge on my thought process.
You have 36 possible outcomes, and in 6 of them you rolled the same number. So your probability is $\frac{30}{36}$.