They gathered 200 people of which 50 were known to have the zombie virus.  of those who had the virus, 48 tested positive.  of those who did not have the virus, 135 tested negatives. determine whether or not the events of having the virus and testing positive are independent.

Let be the set of people infected with the virus, and the set of people who get a positive result (true or false) when tested for the virus. Any person tested for the virus will get one or the other result and not both, so the events and are mutually exclusive:



where denotes the size/cardinality of a set.

We're told that and , which means .

Similarly, we have



and we know and , so .

The probability of each possible event is obtained by dividing the size of each corresponding set by the total 200. So we have the following table:



The events and are independent if . From the table above, we find that



and



which are not equal, so the events are not independent.

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