A box contains five keys, only one of which will open a lock. Keys are randomly selected and tried, one at a time, until the lock is opened (keys that do not work are discarded before another is tried). Let Y be the number of the trial on which the lock is opened.

Find the probability function for Y.

My work: Obviously, the probability of the first key working is 1/5. To find the probability of the first key not working and the second key working, I multiplied (4/5)*(1/4). Similarly, the probability of the first and second keys not working and the third key working is (4/5)*(3/4)*(1/3). Am I on the right track? The probability ends up being 1/5 for each key, and I was concerned because I thought it should be different for each one.

Thanks for your help!