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) till she suceeds 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

Answer: (D)

$\frac{1}{10}$

$P=LLLLLLW$
$P=\frac{9}{10}\times \frac{8}{9}\times \frac{7}{8}\times \frac{6}{7}\times \frac{5}{6}\times \frac{4}{5}\times \frac{1}{4}$
$P=\frac{1}{10}$