Question

A parking lot contains 100 cars , k of which happen to be lemons. we select m of these cars

Answer 1

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 $\frac{k}{100}$

The probability that a car is tested is given by $\frac{m}{100}$

The probability that a car is lemon and it is tested is given by $\frac{n}{m}$

For a conditional probability, the probablility of event A given event B is given by:

$P(A|B)= \frac{P(A\cap B)}{P(B)}$

Therefore, the probability that a car is lemon, given that it is tested is given by.

$P(lemon|tested)= \frac{P(lemon\, and\, tested)}{P(tested)} \\ \\ = \frac{ \frac{n}{m} }{ \frac{m}{100} } = \frac{n}{m} \times \frac{100}{m} = \frac{100n}{m^2}$