A box of products has 4 genuine products and 2 defective products. Choose three products from them.

Then the total number of combinations of three of the six products is C63 (there is no way to write it in standard form, just look, the formula I want to express is the combination number of three of the six products).

Therefore, for the question 1:

The probability that one of the three selected products happens to be defective;

That is, choose one defective product from two defective products, and then choose two genuine products from four genuine products. All combinations in this case are C2 1*C42.

So the probability of the first question is (C2 1*C42)/(C63)=3/5.

For the second question:

The probability that there are at least 1 defective products in the selected 3 products.

Consider his inverse proposition, that is, the three products selected are genuine, and all the combinations at this time are C43.

So the probability of the second question is 1-(C43/C63)=4/5.