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 $kth$ trail is

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

Answer 1

The correct option is B

$\frac{k}{1000}$

Explanation for the correct option:

Find the probability of stranger succession.

Let $E$ be the event of stranger succeeds to open the locker at the $kth$ trial

then, the probability of stranger not succeeds to open the locker is,

$P(E\text{'})=\frac{999}{1000}\times \frac{998}{999}\times \frac{997}{998}\times \dots .\times \frac{(1000-k+1)}{(1000-k+2)}\times \frac{(1000-k)}{(1000-k+1)}$

$P(E\text{'})=\frac{(1000–k)}{1000}$

$\therefore P\left(E\right)=1-\left(\frac{(1000–k)}{1000}\right)$

$=\frac{\mathbf{k}}{\mathbf{1000}}$

Hence, Option ‘B’ is Correct.