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?

Answer 1

`(1)/(270)=0.00370`

Explanation:

As the numbers are only between 1 and 30

Total number of possible combinations = 30×30×30 = 27000

If there are 100 attempts then

`\text{P (someone guesses correct)}=\frac{\text{Number of attempts}}{\text{Total number of possible combinations}}\\\Rightarrow \text{P (someone guesses correct)}=(100)/(27000)\\\Rightarrow \text{P (someone guesses correct)}=(1)/(270)=0.00370`

∴ Probability someone can guess the correct combination given 100 attempts is
`\mathbf{(1)/(270)=0.00370}`