5. A College employs 75 teachers, of whom 47 are full-time and the rest are part-time. Of the 39 male teachers at the College, 26 are full-time.
- Represent this information on a Venn diagram.
- One teacher is selected at random to be interviewed by an inspector. Find the probability that the teacher chosen
- works full-time and is female,
- works part-time, given that he is male.
- Three teachers are selected at random to be observed by an inspector during one day. Find correct to 3 significant figures the probability that
- all three teachers chosen work full-time,
- at least one of the three teachers chosen is female.