A problem in probability theory?

Question

Combinatorics

Hello, I need a fresh look at the problem, I've been sitting for an hour now - I just can't imagine everything correctly and visualize the model. A detailed explanation is welcome :)

The computer test in probability theory consists of tasks on three topics. For the first topic - 4 options for tasks, for the second and third topics - 5 options each. The choice of tasks for testing is made by a computer program randomly. The choice of tasks for each of the topics does not depend on the choice of tasks for other topics.
The student takes the test 3 times.
Let the event A be that when passing the test for the second time, the student will come across one of the questions that came across during the first attempt.
Event B consists in the fact that when passing the test for the third time, the student does not come across any of the questions that came across on the first attempt.
Then the probability that at least one of the events A and B will happen is ...
The answer must be written as a decimal fraction with three decimal places.

Answer 1

Why is there a fresh look, rather old.
Do you seem to be good at c#? So simulate the task, full enumeration - only 4 * 5 * 5 == 100 options, two fingers on the asphalt.

Detailed explanation is welcome :)

trample on

Answer 2

Events A and B are independent. Therefore, the required probability = P(A)+P(B) - P(A and B) = P(A)+P(B)-P(A)*P(B)
It remains to find the probability of each event. With a probability of 1/4 on the first topic, the same question will come up as in the first attempt. In the second and third topic - the probability is 1/5. Here you have 3 asymmetrical coins thrown. All you have to do is find the probability that for A - exactly one coin will be tails, and for B - that all coins come up heads. Is that clearer?