A woman has 10 keys out of which only one opens a lock. She tries the keys one after another (keeping aside the failed ones) till she succeeds in opening the lock. What is the chance that it is the seventh key that works?
My approach so far:
From what I've thought out so far, I think we need to find out the probability of each of the keys failing before the seventh key, and then the probability of the seventh key being the one that works out of the remaining keys (which would be four by the time she reaches the seventh key).
The only problem I'm facing is that I don't understand how to take into account the probabilities of those events happening one after another, simultaneously.