Hotel rooms allocated without replacement

Core stretch

Each unallocated room is equally likely to be assigned to the next guest.

Hotel rooms are numbered 1 to 30 and allocated without replacement.

1. Find the probability that the first guest receives a room number
   1. not more than 18,[1]
   2. prime.[1]
2. A prime-numbered room has been allocated to the first guest. From the 29 remaining rooms, find the probability that the second guest also receives a prime-numbered room.[2]