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A certain three​-cylinder combination lock has 65 numbers on it. To open​ it, you turn to a number on the first​ cylinder, then to a second number on the second​ cylinder, and then to a third number on the third cylinder and so on until a three​-number lock combination has been effected. Repetitions are​ allowed, and any of the 65 numbers can be used at each step to form the combination.​ What is the probability of guessing a lock combination on the first​ try?

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sqdancefan

Answer:

  1/275,625 ≈ 3.641×10^-6

Step-by-step explanation:

There are 65×65×65 = 274,625 possible combinations. The probability of guessing the correct one is 1/275,625 ≈ 3.641×10^-6.

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