False positive

Discrete Mathematics 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 \(C1\)(consumerism-order 1).

Scientists have have devised a machine for testing a person for \(C1\). It identifies \(C1\) in an infected person with \(99\%\) accuracy. It identifies a healthy person as healthy \(95\%\) of the time. The probability of a random person being affected by \(C1\) is known to be \(10^{-4}\).

Find the approximate probability that a person is affected by \(C1\), 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 \(C1\) is best left unsaid.


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