You basically need to look at the various models and see what situation matches the assumptions. For a coin toss or two-outcome set of independent trials, we use binomial. For things that model rates we use Poisson. Without replacement uses other distributions like hyper-geometric.
You have to use a certain amount of judgement to know what probability model to use and you may have to derive it yourself if a common solution does not exist.
Hint: For the first one, you should look into a Binomial because the chance of losing luggage is assumed the same for each piece of luggage and all items are independent of each other.