QUESTION 4 (a) A company employs 12 male and 20 female workers in the manufacturing sector. Among the male workers: 7 are from the Assembly Department, 2 are from the Quality Control Department, and 3 are from the Logistics Department. As for the female workers: 15 are from the Assembly Department, 3 are from the Quality Control Department, and 2 are from the Logistics Department. A worker is selected at random. Find the probability that: i) ii) The worker is a male The worker is from the Assembly Department iii) The worker is a female from the Logistics Department iv) The worker is from the Quality Control Department, given that the worker is male (12 marks) (b) i) ii) Draw the probability tree to find the sample space for the gender of three children in a family. (4 marks) From the probability tree in b(i), what is the probability of getting at least one boy. (4 marks) (c) Given that P(A) = 0.59, P(B) =0.46 and P(A?B) = 0.28, determine; i) P(A’?B) iv) P(A’?B’) ii) P(AUB) v) P(A|B’) iii) P(A?B’) vi) P(B’|A’)