Question

A locker can be opened by dialing a fixed three digit code (between 000 and 999). A stranger who does not know the code tries to open the locker by dialing three digits at random. The probability that the stranger succeeds at the trial is

• A. $\frac { k } { 999 }$
• B. $\frac { k } { 1000 }$
• C. $\frac { k - 1 } { 1000 }$
• D. None of these

Answer 1

Answer: (B)

$\frac { k } { 1000 }$

Answer 2

Let $A$ denote the event that the stranger succeeds at the $k ^ { t h }$ trial. Then

$P \left( A ^ { \prime } \right) = \frac { 999 } { 1000 } \times \frac { 998 } { 999 } \times \ldots . . \times \frac { 1000 - k + 1 } { 1000 - k + 2 } \times \frac { 1000 - k } { 1000 - k + 1 }$

$\Rightarrow$ $P \left( A ^ { \prime } \right)$ $= \frac { 1000 - k } { 1000 }$ ⇒