Four fair dice are marked differently on their six faces. Choose first ANY one of them. I can always choose another that will give me a better chance of winning. Investigate.
Explain why it is that when you throw two dice you are more likely to get a score of 9 than of 10. What about the case of 3 dice? Is a score of 9 more likely then a score of 10 with 3 dice?
Bluey-green, white and transparent squares with a few odd bits of
shapes around the perimeter. But, how many squares are there of
each type in the complete circle? Study the picture and make an
The King of a distant kingdom arranged a marriage for his only
daughter to a prince from a nearby kingdom. However, the Princess
had already fallen in love with a handsome, clever but
unfortunately poor peasant. The king upon learning of the
Princess's relationship with the peasant, ordered the suitor to be
thrown into the lions' den. His daughter pleaded with the king for
mercy and the king offered a compromise. Her lover could walk
through a maze, with each path leading to one of two rooms. In one
room there would be the Princess, but in the other would be a pride
of very hungry lions. If the peasant entered the room with the
Princess, they would be allowed to marry. If the peasant entered
the room with the lions, well, that would be that.
The King showed the Princess a map of the maze and the Princess
was allowed to decide which room she would wait in, either A or B.
She was not allowed to send a copy to her lover, so she knew he
would have to guess which path to follow. Which room should she
wait in to give her lover the greatest chance of finding her? What
is the probability that the story will end happily ever after?
The map of the maze is reproduced below, where the heavy lines
represent corridors of the maze each of which end in a door to a
chamber. The peasant will not know his fate until he opens the
soundproof door and steps into the chamber either to the arms of
his Lady or the jaws of the Lions. Also, the Princess will not hear
him knock and hence open the door.