I have been reading about feature selection for ML models and I saw an explanation why this model presents some issues. For what I know in forward selection you start with a set of features and then, one by one, we check their statistical significance calculating their p-values. If one feature is more significant the others (regarding their p-value) then I add this feature to a list and I remove it from the list of features to be tested. This process continues until there are no more features to test. So if I have a significance level of 0.05, then I could say that the probability of having a false positive is: $$p(false\ positive)=0.05$$ and the probability of no false positive would be: $$p(no\ false\ positive)=1-0.05=0.95$$

If I assume that these events are independent and if I have ten features I will end up with: $$p(\sim false\ positive)=0.95^{10}$$

so the $$p(at\ least\ one\ false\ positive)=1-0.95^{10}=0.402$$

therefore this result that I will have a 40% chance that one feature would be deemed like relevant, but in reality it is not.

The question that I have is how the use of cross validation would help to avoid this issue?