Exercice 1: Soit A, B et C des vnements mutuellement indpendants. Monter que A et B C sont indpendants.

Exercise 2: Consider the electrical circuit below. It is assumed that the components fail independently of each other. 1. What is the probability that the whole circuit works? 2. If the circuit works, what is the probability that component A does not work? Exercise 3: It is assumed that in 2019 Nissan sold three car models in North America: Sentra, Maxima and Pathfinder. Of the vehicles sold, 50% were Sentras, 30% Maximas and 20% Pathfinders. In the same year, 12% of Sentras, 15% of Maximas and 25% of Pathfinders had a particular mechanical defect. 1. If you own a 2019 Nissan, how likely is it to have this defect? 2. An engineer's 2019 Nissan has a mechanical defect. What model is he likely to own?Exercise 4: In a jackpot containing two gray and three yellow tokens, Gad, Mary, Dan and Jeff successively draw a token without putting it back. The rst to draw a gray token wins. What is each player's probability of winning