I am just doing some olympiad exercises to practice my probability skills, but I have difficulties with this one:
Lets consider a village where each resident gets off work at a random time. Afterwards they go fishing. The lake only have two types fishes, $A$ and $B$. $B$ make up a proportion $p$.
This village has a law wich states that you have to stop fishing as soon as you catch the first fish of type $B$.
What proportion of all fish caught in the lake are fishes from type $B$ ?
The first thing I would do is to calculate the probability of catching fish $B$, which is equal to $p$. Now I do not how the include the other information?