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
`(k)/(100)`

The probability that a car is tested is given by
`(m)/(100)`

The probability that a car is lemon and it is tested is given by
`(n)/(m)`

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


`P(A|B)= (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)= (P(lemon\, and\, tested))/(P(tested)) \\ \\ = ( (n)/(m) )/( (m)/(100) ) = (n)/(m) * (100)/(m) = (100n)/(m^2)`