Given that a parking lot contains 100 cars, k of which happen to be lemons.
This is a conditional probability question.
Let event A be that a car is tested and event B be that a car is lemon.
The probability that a car is lemon is given by [tex]\frac{k}{100}[/tex]
The probability that a car is tested is given by [tex]\frac{m}{100}[/tex]
The probability that a car is lemon and it is tested is given by [tex]\frac{n}{m}[/tex]
For a conditional probability, the probablility of event A given event B is given by:
[tex]P(A|B)= \frac{P(A\cap B)}{P(B)} [/tex]
Therefore, the probability that a car is lemon, given that it is tested is given by.
[tex]P(lemon|tested)= \frac{P(lemon\, and\, tested)}{P(tested)} \\ \\ = \frac{ \frac{n}{m} }{ \frac{m}{100} } = \frac{n}{m} \times \frac{100}{m} = \frac{100n}{m^2} [/tex]
