Question

In a viral pool test it is known that in a group of five (5) people, exactly one (1) will test positive. If they are tested one by one in random order for confirmation, what is the probability that only two (2) tests are needed? 

Answer 1

$$P(X=2)=\dfrac{5-1}{5}(\dfrac{1}{5-1})=\dfrac{1}{5}$$