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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. If P is the probability that the stranger succeeds at the K^th trail, find 1000p. ( Assume that the stranger does not repeat unsuccessful combinations)

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Detailed Solution

Let A denote the event that the stranger succeeds at the K^th trail, then

$p = P (A) = \frac{999}{1000} \times \frac{998}{999} \times ....$

$\times \frac{1000 - K + 1}{1000 - K + 2} \times \frac{1}{1000 - K + 1}$

$\Rightarrow p = \frac{1}{1000} \Rightarrow 1000 p = 1$

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