Exercise 1: Let A, B and C be mutually independent events. Mount As A and B U C are independent. Exercise 2: Consider the electrical circuit below. It is assumed that the components fail independently of each other. 1. What is the probability of the whole circuit working? 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 models of cars in North America: Sentra, Maxima and Pathfinder. Of the vehicles sold, 50% were Sentra, 30% Maxima and 20% Pathfinder. In the same year, 12% of the Sentra, 15% of the Maxima and 25% of the Pathfinder 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. Which model is likely to possess?Exercise 4: In a jackpot containing two gray chips and three yellow ones, Gad, Mary, Dan and Jeff successively pull a chip without handing it over. The rst person to draw a gray token wins. How likely is each player to win? Exercise 5: Let Xbe a random variable with a density function of: ( lozZ2x+5if0 5x51 X) = 2 O elsewhere 1. Find normalization constant k. P 2. Calculate the standard deviation of the random variable Y: 2/X+ 3 E00. 3. Determine the allocation function of X