KöMaL 2023 B5306

We have a weighted (six-sided) die and a weighted coin. On one side of the coin there is one dot, and on the other side there are two dots. The expected value of the number of dots appearing on top is the same for the die and the coin. Show that if the die and the coin are thrown simultaneously then the probability of getting more dots on the coin than on the die is greater than the probability of getting more dots on the die than on the coin.