Question from DragonLord:

Question from DragonLord:

So today, I was playing a dice game with my friend.

I roll a die, and he rolls a die. He told me the probability that he rolls a higher number than me is 1/2, (the die are standard six sided ones).

Is he right or wrong?

$\begin{array}{|r|r|r|r|r|r|r|r|} \hline \text{he}\rightarrow & 1 & 2 & 3 & 4 & 5 & 6 \\ \text{you}\downarrow \\ \hline 1 & & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark \\ \hline 2 & & & \checkmark & \checkmark & \checkmark & \checkmark \\ \hline 3 & & & & \checkmark & \checkmark & \checkmark \\ \hline 4 & & & & & \checkmark & \checkmark \\ \hline 5 & & & & & & \checkmark \\ \hline 6 \\ \hline \end{array} \\ \qquad \checkmark = \text{heigher}$

The probability that he rolls a higher number than me is  $\mathbf{\dfrac{15}{36}=\dfrac{5}{12}}\quad (0.41.\overline{6}\ \%)$