# 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 $C1$(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.

×