2015 TJC H1 P2 Q8

In a school, there are \(28\) and \(18\) teachers in the Science and Mathematics Departments, respectively. Of the \(28\) Science teachers, there are \(10\)single men, \(4\) single women, \(2\) married couples, \(8\) married men and \(2\) married women. Of the \(18\) Mathematics teachers, there are \(3\) single men, \(1\) married couple, \(5\) married men and \(5\) married women. No Science teacher is married to a Mathematics teacher. Two teachers are chosen from the two departments to attend a focus group discussion.

Find the probability that

1. they are married to each other,[2]
2. they are a man and a woman in the same department,[2]
3. they are married to each other given that a man and woman and chosen,[2]
4. they are from different departments given that a married man and single woman are chosen.[3]