Ryan invented a game called "Magic 5" in which you get points if you get the same result multiple times in a row. He put two identical balls, one black and one white, inside a dark bag. The player must draw one ball at a time and replace it. The outcomes gain or lose points according to the following table: Same outcome as previous draw Different outcome than previous draw First Result -- -- Second Result +2 points -2 points Third Result +3 points -2 points Fourth Result +4 points -2 points Fifth Result +6 points -2 points What is the most probable outcome if you play this game? Use a mathematical proof to explain the previous answer.

Accepted Solution

In this game called “Magic 5” there is no probable outcome when you play this game. The possibility of having the same outcome as the previous draw and having a different outcome than the previous draw is both 50%. Thinking that in the first draw you get a white ball, in the second draw you have a 50% chance to get a while ball again and a 50% chance of not. It’s the same as in the next draw; you’ll have 50% of it having the same outcome and 50% having a different one. And it goes and on, that’s why there is no probable outcome in this game rather the two choices has the same chance.