Probability of events when two different colored dice are thrown.

Two six-sided dice are thrown, one blue and one red. Calculate probability of events:

$a)$ $P($red die is $5|$ sum of scores is $8)$

$b)$ $P($either die is $5|$ sum of scores is $8)$

There are more but with these I will be able to figure the rest out.

My answer for problem $a)$ is $1/6$. Is that correct also?

• Generally, you are expected to show your work. This is especially useful if you want a quick answer since users can proofread your work instead of doing it from scratch. And you get to see where your mistake happened, if there are any. Formatting tips here. – Em. Sep 7 '16 at 15:17

a) There are $5$ different ways to obtain $\color{blue}{X}+\color{red}{Y}=8,$ namely $$\{\color{blue}{X},\color{red}{Y}\}=\cases{\color{blue}{2},\color{red}{6}\\ \color{blue}{3},\color{red}{5}\\ \color{blue}{4},\color{red}{4}\\ \color{blue}{5},\color{red}{3}\\ \color{blue}{6},\color{red}{2}\\}$$
whereof only one has a red $5$, so the probability would be $\frac{1}{5}.$
b) That either die is $5$ (still when they sum to $8$) is seen in two of the cases above, so the probability is $\frac{2}{5}.$