How much more likely is getting a prime number than a triangular number from a list of numbers from 1 to 100?

Question

From a list of numbers from 1 to 100, how much more likely is it to get a prime number than a triangular number?

Solution:

There are $25$ prime numbers between $1 - 100$ so $25$%

There are $13$ triangular numbers between $1 - 100$ so $13$%

$\frac{(25 - 13)}{25}$

So it's $48$% more likely

Is this correct?

Answer 1

You know that the chance of picking a prime number is $25\%$. You know that the chance of picking a triangular number is $13\%$. You are looking for the difference in probabilities, therefore you should perform a subtraction. $$25\%-13\%=\frac{25}{100}-\frac{13}{100}=\frac{25-13}{100}=\frac{12}{100}=12\%$$ Therefore it is $12\%$ more likely that you will pick a prime number than a triangular number. No need to divide by $25$. Hope this helps!