# a women has 10 keys out of which 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 the 7th key works??

SHAIK AASIF AHAMED
8 years ago
Hello student,
If the 7th key is correct, the first six are incorrect.
. .(and we don't care about the last three.)

So, we want:.no - no - no - no - no - no - yes.

The probability is:.$\frac{9}{10}\cdot\frac{8}{9}\cdot\frac{7}{8}\cdot \frac{6}{7}\cdot\frac{5}{6}\cdot \frac{1}{5}$

. .which reduces to:.$\frac{\rlap{/}9}{10}\cdot\frac{\rlap{/}8}{\rlap{/}9}\cdot\frac{\rlap{/}7}{\rlap{/}8}\cdot \frac{\rlap{/}6}{\rlap{/}7}\cdot\frac{\rlap{/}5}{\rlap{/}6}\cdot \frac{1}{\rlap{/}5} \;=\;\frac{1}{10}$
Thanks and Regards
Shaik Aasif