Answer:
a. Kth = 1/n, 1/n-2, 1/n-3,..........
b. Kth= 1/n!
Explanation: This is a mathematics probability and combination problem. It can only be solved using probability and combination rules.
Kth means the number of try she is probably to apply before she can open the door.
For the first problem, heartfilia tries the keys and discard the ones that doesn't open the door. that means for the first time her probability of opening the door is 1/n and for the second time her probability will be 1/n-1 and for the third time it will be 1/n-2, so will her probability of opening the door increases until she gets to the last key which probability will be equal to 1, Therefore the chances she will have to open the door will increase as she tries the key at random,disregarding the ones she has tried before.
The second question involves combination, because she doesn't disregard the ones she has tried before, she may keep trying 1 key many times, since she picks up the key at random. It means that the chance she has to open the door remains the same till she gets the right key. And each try is 1/n! Which means that they is probability of picking up the same key many times, which has reduced her chances of getting the right key.
