Hi guys, I've been working on a mathematical model all day and I've lost the ability to think. I've hit a wall. So, I've taken a brake and reformulated the problem into a puzzle. Can anyone shed some light? I'm going to bed and I look forward to your replies in the morning.
The ball bag problem
A room contains an empty bag and a box that contains an infinite number of balls. The balls within the box are coloured and there are an infinite number of colours used, possibly repeatedly. You and another person enter the room. You stand facing the wall so you canít see the bag, the box or the other person. You also have a piece of paper and a pen. The other person then removes an arbitrary number of balls from the box and places them into the bag. The number of balls removed and the colour of the balls is completely up to the other person. When the other person places a ball into the bag, they call out the colour of the ball and you note it down on the paper. However, you know that the other person lies about the colour of the ball 30% of the time. Once the other person has finished placing balls into the bag, they close it, give it a shake and then select a ball at random from it. What colour do you expect the ball to be and how sure are you?