A probability experiment
Imagine you have a bag containing 100 plastic tokens. Some are square, some are circular. Some are red, some are blue. To be precise:
- 80% of the tokens are squares, the rest are circles.
- Of the square tokens, 75% are red and 25% are blue.
- Of the circle tokens, 10% are red and 90% are blue.
Now suppose someone takes a token from the bag, without you seeing it. They tell you it is blue, and ask you to guess the shape. Given that 90% of the circles are blue, many people might well guess that the shape is almost certainly a circle. In this article, we will see why that logic is flawed.