Suppose the mechanical parts produced in a factory are defective with probability p= 0.02, independently of each other. The factory sells the parts in boxes of 50 pieces and has to pay a fine in case two or more defective parts are found among the 50 pieces. 1. Define the model of the probability distribution of the random variable X: “Number of defective pieces in the box”. What is the probability that in a box of 50 pieces there are two or more defective parts?
2. Assuming that the number of defective pieces in a given box is independent of the other boxes, what is the probability that out of 10 packages there is one with two or more defective pieces?