What are the likelihoods of different events when you roll a dice?

Which of these ideas about randomness are actually correct?

Identical discs are flipped in the air. You win if all of the faces show the same colour. Can you calculate the probability of winning with n discs?

Can you generate a set of random results? Can you fool the random simulator?

The King showed the Princess a map of the maze and the Princess was allowed to decide which room she would wait in. She was not allowed to send a copy to her lover who would have to guess which path. . . .

What is special about dice?

How can we use dice to explore probability?

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?

Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?