There are 10 keys and only one of them can open a lock We do

There are 10 keys and only one of them can open a lock. We do not know which key can open the lock, but we will try them one by one until we find the right key. We record the key(s) which we have already tried.

(a) What\'s the probability of finding the right key in the first trial?

(b) What\'s the probability of finding the right key in the third trial?

(c) If we know that the first two keys we tried are not the right key, what\'s the probability of finding the right key in the next/third trial?

Solution

(a) The probablity is (1/10), as 1 out of the 10 keys is the right one.

(b) Here too, the probablity remains (1/10), as we do not reject the previous keys (we choose from a bowl of 10 again)

(c) Now the probablity increases to (1/7) or in the general case (1/n-1), as we have discarded the previous keys and have an equal chance of finding the right key in the remaining keys!