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

Answer:

$\frac{1}{270}=0.00370$

Step-by-step 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

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

∴ Probability someone can guess the correct combination given 100 attempts is $\mathbf{\frac{1}{270}=0.00370}$