Twelve lettered tiles spelling the word TRIGONOMETRY are placed inside a bag. T R I G O N O M E T R Y

1. (a)A tile is taken at random from the bag. Find the probability that the tile shows a letter R. Give your answer as a fraction in its simplest form.[1]
2. (b)All the tiles are placed back in the bag, a tile is then taken at random and placed on the table. A second tile is taken at random and placed to the right of the first tile. A third tile is taken at random and placed to the right of the second tile. 1st 2nd 3rd Find the probability that, in the order the tiles were placed on the table, they spell GET.[2]
3. (c)Vowels are the letters A, E, I, O and U. All other letters are consonants. All the twelve tiles are placed back in the bag and two tiles are taken at random, without replacement.
4. (c)(i)Complete the tree diagram.[2]
5. (c)(ii)Find the probability that the tiles both show vowels.[1]
6. (c)(iii)Find the probability that one tile shows a vowel and one tile shows a consonant.[2]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.