Question

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) until she succeeds in opening the lock. What is the chance that it is the seventh key that works?

• A. $\frac{7}{10}$
• B. $\frac{1}{2}$
• C. $\frac{3}{10}$
• D. $\frac{1}{10}$

Answer 1

The correct option is D $\frac{1}{10}$

If the 7th key is correct, the first six are incorrect.

The probabiity is $\frac{9}{10}\times \frac{8}{9}\times \frac{7}{8}\times \frac{6}{7}\times \frac{5}{6}\times \frac{1}{5}=\frac{1}{10}$