Editing Bayes' theorem (section)

===Cancer rate===
If all patients with pancreatic cancer have a certain symptom, it does not follow that anyone who has that symptom has a 100% chance of getting pancreatic cancer. Assuming the incidence rate of pancreatic cancer is 1/100000, while 10/99999 healthy individuals have the same symptoms worldwide, the probability of having pancreatic cancer given the symptoms is 9.1%, and the other 90.9% could be "false positives" (that is, falsely said to have cancer; "positive" is a confusing term when, as here, the test gives bad news).

Based on incidence rate, the following table presents the corresponding numbers per 100,000 people.
{| class=wikitable
! {{diagonal split header|Cancer|Symptom}}
! style="width:5ex;"|Yes
! style="width:5ex;"|No
! rowspan="5" style="padding:0;"|
! Total
|-
! Yes
| style="text-align:right" | 1
| style="text-align:right" | 0
| style="text-align:right" | 1
|-
! No
| style="text-align:right" | 10
| style="text-align:right" | 99989
| style="text-align:right" | 99999
|-
| colspan="5" style="padding:0;"|
|-
! style="width:15ex;"|Total
| style="text-align:right" | 11
| style="text-align:right" | 99989
| style="text-align:right" | 100000
|}
Which can then be used to calculate the probability of having cancer when you have the symptoms: 
:<math>
\begin{align}
P(\text{Cancer}|\text{Symptoms}) &= \frac{P(\text{Symptoms}|\text{Cancer}) P(\text{Cancer})}{P(\text{Symptoms})} \\
 &= \frac{P(\text{Symptoms}|\text{Cancer}) P(\text{Cancer})}{P(\text{Symptoms}|\text{Cancer}) P(\text{Cancer}) + P(\text{Symptoms}|\text{Non-Cancer}) P(\text{Non-Cancer})} \\[8pt]
&= \frac{1 \times 0.00001}{1 \times 0.00001 + (10/99999) \times 0.99999} = \frac1{11} \approx 9.1\%
\end{align}</math>