False positive

Probability Level 3

A new disease has been identified in the human population. For the sake of the following discussion, we will refer to it as C1C1(consumerism-order 1).

Scientists have have devised a machine for testing a person for C1C1. It identifies C1C1 in an infected person with 99%99\% accuracy. It identifies a healthy person as healthy 95%95\% of the time. The probability of a random person being affected by C1C1 is known to be 10410^{-4}.

Find the approximate probability that a person is affected by C1C1, given that his/her test returned positive.

Note: The data given in this problem are representative. The actual probability of a random human to be affected by C1C1 is best left unsaid.


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