Simple dice questions. There are two dice.
Assume dice are fair.
What does the following probability represent:
It's $$\frac{1}{6} + \frac{1}{6} - \left(\frac{1}{36} \right)$$
What does this represent:
$$\frac{1}{6} \cdot \frac{5}{6} + \frac{1}{6} \cdot \frac{5}{6}$$
This represents the probability of rolling just a single $X$ (where $X$ is a specified number on the dice, not a combined value where $X$ is between $1$ and $6$) right?
What does this represent: $1- \left(\frac{5}{6} \cdot\frac{5}{6} \right)$
What does 
1/6 + 1/6 - 1/36 represent? Is this also the probability of rolling a single 6? If so, why do we subtract the 1/36 at the end (the probability of rolling both sixes). Don't we want to include that possibility since we're looking for the probability of rolling a single 6?
 A: The first one is the probability that a number, say 3, comes on any one of the two dice.
A: 1) is the chance you get at least one of a given number in two rolls.  The two $\frac 16$ are the chance of getting it on the first and second roll, but you have double counted the case where you got it both times, so subtract that once.
2) is the chance you get exactly one of a given number in two rolls.  The first term represents getting it on the first roll and not on the second.  The second term is the reverse.
3) is again the chance you get at least one of a given number in two rolls, calculated this time by subtracting the chance that you don't get it on either roll from $1$.
A: Assuming the dice have 6 sides each, all of which are equally likely:
$(\frac{5}{6} \cdot\frac{5}{6})$ is the odds of rolling one of five particular sides, and then also one of five particular sides (though those two sides need not be the same). It's the chance of not rolling side A twice in a row.
1-p is just the chance of that not happening. Therefore $1-(\frac{5}{6} \cdot\frac{5}{6})$ is the chance of not not rolling side A twice in a row.
A: 1> Same as 3. [but used the inclusion exclusion principle]
2> P[You get different outcomes on rolling the pair of dice twice]
3> P[you get a particular outcome atleast once]
