A locker can be opened by dialing a fixed three digit code (betwe… - Vidyadip

MCQ

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 ${k^{th}}$ trial is

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

✓

Answer

Correct option: B.

$\frac{k}{{1000}}$

b
(b) Let $A$ denote the event that the stranger succeeds at the ${k^{th}}$ trial. Then

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

$ \Rightarrow $$P(A')$$ = \frac{{1000 - k}}{{1000}}$

$⇒$ $P(A) = 1 - \frac{{1000 - k}}{{1000}} = \frac{k}{{1000}}.$

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