. A manufacturer uses three different suppliers for a particular component. In current inventory, there are 450 parts from supplier A, 350 from supplier B, and 200 from supplier C. The manufacturer found that 0.2\% of parts from supplier A is defective; 0.51% of parts from supplier B is defective; 0.61% of parts from supplier C is defective. Let A, B, C denote the events that the part came from supplier A, B, C, respectively. 1 Based on the inventory mix, determine P(A), P(B), P(C). 2. If one randomly selected part is defective, determine the probability that it came from supplier C.

Dr. Cy Clopps is ophthalmologist and owner of the Spex Appeal Eye Clinic.  A review of 100 patient’s records indicated that 30 of these patients have vision insurance.  Further, 35 of the 100 patients got bifocal glasses but had no insurance.  Finally, 10 of the 100 patients had insurance but did not get bifocals.  d.  Of those with insurance, what proportion got bifocals? e.Are the events independent?  Mutually exclusive?  Collectively exhaustive?

9. A law firm employs three types of lawyers: junior lawyers, senior lawyers, and partners. During a given year, there is a 0.1 probability that a junior lawyer will be promoted to senior lawyer and a 0.05 probability that he or she will leave the firm. Also, there is a 0.2 probability that a senior lawyer will be promoted to partner and a 0.15 probability that he or she will leave the firm. There is a 0.03 probability that a partner will leave the firm. The firm never demotes a lawyer. th Let Xn be the status of an employee at the n' year after he or she has been hired, it could be one of the three types of lawyers (junior, senior, or partner) or two types of leaving (either leaving as a partner or leaving as a non-partner). Let state 0-junior, state 1-senior, state 2=partner, state 3= leave as non-partner, state 4= leave as partner The (one-step) transition matrix is P = 0.85 0 0 0 0 0.1 0 0.05 0.65 0.2 0.15 0 0.97 0 0 1 0 0 0 0 0 0 0.03 0 1 (a) Use the fundamental matrix method,…

Thirty-five percent of the cars in Israel are new. Out of the new cars, 60% are white. Overall, 45% of the cars in Israel are white. If event A is “New” and event B is “White”, which of the following is correct? a. There is not enough data to answer the question. b. Events A and B are dependent. c. Events A and B are independent d. Event A and B are mutually exclusive.