Question

You are trying to devise a game where you win and lose with equal probability (50% each). You like marbles, so you come up with this game: put marbles of two different colors in a bag. If you draw two marbles of the same color, you win. If you draw two different color marbles, you lose.

You have a three blue marbles and an unlimited number of green marbles. If you put all three blue marbles a bag, how many green marbles should you use to make the game fair?

a. Many people intuitively would say three is the right answer. Show that it is not by calculating the win & lose probabilities for having three blue and three green marbles.

b. Find a right answer. Describe how you found the answer. Show that it is right by calculating the win & lose probabilities.

Answer 1