If your first try of opening the lock fails, what is the probability that your second try succeeds?

Is the answer $\frac{2}{256}$ because you get to try two combos, or is it $\frac{1}{255}$ because you get to try one combo from 255 remaining?

I'm confused and not sure which is correct

  • $\begingroup$ Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level. $\endgroup$ – user64742 Sep 23 '16 at 2:20
  • 1
    $\begingroup$ In this case I think the question includes sufficient thoughts from the asker. It's mainly a question of which understanding of the original problem is correct. $\endgroup$ – David K Sep 23 '16 at 12:22

The probability that your second try succeeds given that the first failed is 1/255. The probability of succeeding on at most two tries is 2/256.


Initially there are $256$ possibilities, the first failure disclose that the code is certainly not the right combination and should be avoided. Hence he should only choose $1$ out of the remaining $255$ possibilities.

The answer is $\frac{1}{255}$ assuming that the person has learned his lesson and remember the earlier combo to avoid.


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