A group of 32students went on a trip to Paris. When they returned, their teacher asked them if they had climbed to the top of the Eiffel Tower (E), visited the Louvre Museum (L) or taken a boat on the River Seine (S). The students replied as follows:

12students had done all three

15 students climbed the Eiffel Tower and took a boat on the Seine

8 students climbed the Eiffel Tower and visited the Louvre Museum but did not take the boat

5 students climbed the Eiffel Toweronly

2 students visited the Louvre Museumonly

1student took a boat on the Seineonly

All32 students did at least one of the threeactivities.

(a)Draw a Venn diagram to represent this information

(b)Find the number of students who went to the Louvre and took a boat trip on the Seine but did not climb to the top of the Eiffel Tower.

(c)Calculate the probability that a student chosen at random:

(i)climbed to the top of the Eiffel Tower

(ii)didtwo of the three activities, but not all three

(iii)visited the Louvre, given that he did only two of the three activities.

(d)A student chosen at random took a boat trip on the Seine.

Find the probability that she also visited the Louvre Museum.