In this experiment, you will draw balls one at a time from a box and, after each draw, estimate the probability that the current box is the Blue Box.
The two boxes:
Blue Box
๐ต๐ต๐ต๐ต๐ต
๐ต๐ด๐ด๐ด๐ด
60% Blue /
40% Red
Red Box
๐ด๐ด๐ด๐ด๐ด
๐ด๐ต๐ต๐ต๐ต
60% Red /
40% Blue
How the box changes:
After each round, the box may change colour.
The current box remains the same colour with probability 20%,
and switches to the other colour with probability 80%.
Your task:
Both the ball counts and the transition probabilities are known to you throughout the task. After observing each ball, you will be asked to report a number between 0 and 100 representing your percent belief that the box just drawn from is the Blue Box.
Your response should take into account both the colour of the ball you just observed and the possibility that the box may have switched since the previous draw.
At the start of the experiment, each box is equally likely to be drawn.