2A 2B 2C
1A 1B 1C
(i) Look at the different options. One could be staying in any of the rooms (2A or 2B or 2C or 1A or 1B or 1C). Let's look at the rooms next door.
2A = 2B
2B = 2A, 2C
2C = 2B
1A = 1B
1B = 1A, 1C
1C = 1B
There are 8 possibilities for being next door and 6 x 5 (30) possible room combinations.
8/30 = 4/15
Answer: 4/15
(ii) Think about it by using one example.
If one is staying on the top floor, what is the probability that the other one is staying on the bottom floor? 3 rooms on bottom floor out of 5 rooms left (3/5)
Answer: 3/5
(iii)
Part (i) was the opposite of this question. Since that answer was 4/15, then subtract that from 1.
1 - 4/15 = 15/15 - 4/15 = 11/15
Answer: 11/15
