yes I made these up, so don't be too harsh on me
Warmup Problem
You have a bag with 20 smooth, spherical stones. Each stone has a 1/2 chance to be either white or black. You draw 19 black stones in a row out of the bag... what is the probability that the final stone in the bag is black?
Problem One
You have two bags... one with 9 black stones and 1 white stones, and another with 1 black stone and 9 white stones. You arrange the two bags into a random order, and then draw from the first one: you pull out a black stone. What is the probability that you will draw a white stone from the second bag?
Problem Two
You have three bags this time... one with 9 black and 1 white, one with 1 black and 9 white, with the third bag containing 5 black stones and 5 white stones. You arrange the bags into a random order of 1-2-3 and then draw from bag 1: you remove a shiny black stone from the bag. You then draw from the second bag... what is the probability that you will draw a white?
Problem Three
You have 3 bags again- the same 3 bags from problem two. Put them in a random order of 1-2-3, and draw randomly from the first bag. Place this stone into the second bag, shake the second bag, and then draw randomly from the second bag. Put the stone you just drew into the third bag, shake the third bag, and then draw from the third bag. What are your chances of drawing a white from the third bag?
Problem Four
You have one bag, with 3 white stones and 1 black stone. You and your friend decide to play a little game... you have two stones (white and black) in your pocket, and he has two stones (white and black) in his pocket. You put one of your stones into your hand as a prediction of what will be drawn out of the bag. Your friend puts one of his stones into his hand as a prediction of what color stone will be in YOUR hand. Then both of you reveal your stones at the same time. If your friend predicted right, he wins. If he didn't, and you guessed correctly, you win. If you NOR your friend guessed correctly, nobody wins. What color stone should you put in your hand?