learnmath.bernatchez.net

Two restaurants, Centre and Nouveau, serve fish sandwiches and salads.

Let \(F\) be the event "a customer chooses a fish sandwich".

Let \(S\) be the event "a customer chooses a salad".

Let \(N\) be the event "a customer chooses neither a fish sandwich nor a salad".

At restaurant Centre, \(P(F) = 0.31 ; P(S) = 0.62 ; P(N) = 0.14\).

1. Show that \(P(F \cap S) = 0.07\).
2. Given that a customer chooses a salad, find the probability that this customer also chooses a fish sandwich.
3. Are events \(F\) and \(S\) independent? Justify your answer.

At restaurant Nouveau, \(P(N) = 0.14\). Twice as many customers choose a salad as a fish sandwich. Choosing a fish sandwich is independent of choosing a salad.

4. Find the probability of choosing a fish sandwich.