There is a rare mineral that is available in 1% of rocks. Anna has a detector that never fails to detect that mineral. Otherwise, it is accurate 90% of the time, i.e. 10% false positive. She puts the device on a rock, and it goes off. She collects it and makes an offer to her colleague Ben to sell the rock for $100. Should Ben take that offer if the value of the mineral is $1000?
chance of the rock is rare = 1 x 0.01 / (1 x 0.01 + 0.1 x 0.99) = 0.0917
If the probability of success is 0.0917, then the expected value of the gamble is 0.0917 x 1000 = 91. So paying $100 is not worth it.
