Question

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.

Answer 1

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.