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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

k999

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B

k1000

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C

k-11000

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D

None of these

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Solution

The correct option is B

k1000


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')=9991000×998999×997998×.×(1000-k+1)(1000-k+2)×(1000-k)(1000-k+1)

P(E')=(1000k)1000

P(E)=1-(1000k)1000

=k1000

Hence, Option ‘B’ is Correct.


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