Question

A combination lock requires a user to select three numbers to unlock it, where all three numbers are between 1 to 30, inclusive, and numbers can be used more than once. What is the probability someone can guess the correct combination given 100 attempts?Write your answer as a fraction.

Answer 1

Note that you can repeat numbers.

3 numbers between 1 to 30 including 1 and 30.

that means (30-1)+1=30 numbers.

3 slots that can be repeated, so there is the following number of combinations:

`30^{3\text{ }}=\text{ }27000`

in 100 attempts, that is a 100/27000=1/270 chance or about 0.37% chance. We can conclude that the correct answer is:

`(100)/(27000)\text{ = }(1)/(270)\text{ }`