How to calculate the probability of answering at least 1 question correctly in a test?

Question

Mathematics

Recently, I wanted to know the probability of answering at least 1 question correctly in a test, where there are only 5 questions, each of which has 4 possible answers.
I did the calculations, which you can see here .

After that, I wrote a script that makes 5 iterations and on each of them, it generates a random number from 1 to 4 (inclusive) and after all iterations, the script checks if there was at least one unit in the list of generated numbers. If yes, then it increases n by 1. All of the above is repeated a huge number of times (100,000,000), and then n is divided by 100,000,000 and multiplied by 100. Thus, we get the probability of correctly answering at least 1 question.

The problem is that according to my calculations, this probability is ̶6̶7̶.̶2̶4̶%̶ 76.27%, and the simulation says that the probability is ̶7̶6̶.̶2̶7̶%̶ 67.24% .
What to believe and where is the mistake?

PS The results of calculations and simulations were written incorrectly above, I mixed them up

Answer 1

P = 1 - 0.75 ⁵ = 0.7627