1.. Based on experience, the probability that a BS Math student of a certain university will shift to another degree program in his 2nd year is 0.06. For the First Semester of AY 2022-2023, the university expects to have 35 freshies in the BS Math program, From this batch, the university aims to produce at least 85% sophomores in the BS Math program, that is, at most 15% will leave the program after one year. What is the probability that this goal will be achieved? a). Mr. Bean buys batches of / electronic components for his invention. Before a batch is accepted, n of the components are selected at random from the batch and tested. If more than * components in the sample are found to be substandard, the batch is then rejected. (a) Find the probability that a batch, which actually contains five substandard components, is rejected when N = 30, n =5 and k = 1. (b) Find the probability that a batch, which actually contains ten substandard components, is rejected when / = 60, n = 10 and k = 1. b). An automobile manufacturer is concerned about a fault in the braking mechanism of a particular model. The fault can, on rare occasions, cause a catastrophe at high speed. The distribution of the number of cars per year that will experience the catastrophe is a Poisson random variable with A = 10. (a) What is the probability that 5 cars per year will experience a catastrophe? (b) What is the probability that more than 3 cars per year will experience a catastrophe? (c) What is the probability that 8 to 12 cars per year will experience a catastrophe