Lesson 11

I propose the following game to you. Choose one of the three dice: \[A=[2, 6, 7, 2, 6, 7],\ B=[1, 5, 9, 1, 5, 9],\ C=[3, 4, 8, 3, 4, 8].\] After that, I will take one of the remaining two, and we will roll the dice. The winner is the one who rolls a higher number. Which die will you choose?

To make an informed choice, you will want to calculate the probability that the number rolled on one die is greater than the number rolled on the other die. For two dice \(X\) and \(Y\), we say that \(X \succ Y\), if when rolling these two dice, the number rolled on \(X\) is greater than the number rolled on \(Y\) with a probability greater than \(\frac{1}{2}\).

Problem. Mark all correct statements.