a woman has 10 keys out of which only one opens a lock.she tries the keys one after the 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
Each time she uses a key, the probability that she chooses the correct one increases.
Let X be the key number which fits.
$\displaystyle P(X = 7) = (\frac{9}{10})(\frac89)(\frac78)(\frac67)(\frac56) (\frac45)(\frac14)$
In brief, you'll see that $\displaystyle P(X = n) = \frac{1}{10}$