please answer for a,b,c

[5 marks] For over a year, employees at company XYZ were working from home due to COVID related restrictions and safety concerns. The company is preparing for work, once the conditions have become safe and restrictions are lifted. As such, XYZ company wishes to study where their employees prefer to work: Work from Home, Work From the Office, or Hybrid work (Home & Office). The company believes this is related to age group (50 and under, over 50). A random sample of 200 employees provides the data shown below. Preferred Work Location Work from Hybrid Home Work 50 and under Over 50 Total a) [2 marks] If one employee is randomly selected from the study, what is the probability that they are over 50 or prefers working from home? b) [1 mark] If an employee selected prefers working in the office, what is the probability that they are over 50? [2 marks] Suppose one employee is randomly selected from the study. i. Are the events A = {the employee over 50} and B = {the employee prefers work from home} mutually exclusive (i.e. disjoint)? Justify your answer using probability. ii. Are the events A = {the individual over 50} and B = {the individual prefers work from home} independent? Justify your answer using probability