Question

I have a lockbox with the digits 0-9 on it. The passcode is 5 digits, repeats...

I have a lockbox with the digits 0-9 on it. The passcode is 5 digits, repeats are not allowed, and order doesn't matter (I just have to have the correct 5 digit buttons depressed).  

A. If I guess at the code, what is the probability that the box will open?

B. If I have completely forgotten the code, what is the probability that it will take less than 10 tries to get it open?

Math   Statistics-And-Probability   
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Answer #1

There are 10 digits and digits cannnot be repeated and order does not importanat so number of possible different passcodes is:

C(10,5) = 10! / (5! *5!) = 252

A:

Out of these possible passcodes only one is correct so the probability that the box will open is a try is

P(open) = 1 / 252= 0.003968

B:

Out of these 252 possible passcodes 251 are correct and 1 is correct. The probability that it will take less than 10 tries (that is 1, 2, 3..or 9 tries) to get it open is

Hence, the required probability is 0.0357143.

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