Question

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?

Answer 1

a) P(finding the right key on first trial) = 1/10 = 0.1

b) P(finding the right key on third trial) = P(not finding the right key on first 2 trials and finding the right key on trial 3)

= 9/10 x 8/9 x 1/8

= 0.1

c) P(finding the right key on third trial | first two keys were not right) = 1/(10-2)

= 1/8

= 0.125