Bonsoiiiir!! J’ai vraiment besoin d’aide, mon prof m’a donné cette exercice noté en math sauf que c’est en anglais, depuis je n’arrive pas. Merci d’avance!! :)

The manager of a sports store has received a supply of running shoes. 5 % of the boxes have been damaged because
of the rain during the trip.
The manager thinks that:
•60% of the damaged boxes contain at least one damaged shoe.
- 98% of the undamaged boxes do not contain any damaged shoe.
A runner buys one pair of shoes. We denote E the event "The box is damaged* and A the event "The box contain
at least one damaged shoe".
1. Find the following probabilities P(E), P(E), P (A) and P(A).
2. Prove that P (A) = 0.4 and work out P (A).
3. Represent this information on a tree-diagram.
4. Find P(A).
5. The customer realizes that one of the shoes he has bought is damaged.
Prove that the probability that the shoe comes from a damaged box is greater than 60%.