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?

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 $\frac{2}{5}.$