lotto chances when knowing 1 number How would I calculate the chances of winning a rigged lotto when I know 1 number already. I know how to calculate the chances without the Conditional, which is with a lotto for exmple 5 picks out of 40 P(0 right) = choose (5,0) * choose (35,5) / choose (40,5) p(1 right) = choose (5,1) * choose (35,4) / choose (40,5) ..... However how would I do this with condition that I already know 1 number ? P(A|B) = p(A AND B) / P(B) So how would I do this with the above exemple of knowing already 1 number because it is rigged ?

If the lottery numbers are random $5$ out of $40$, but you already know one, then you'll still need to choose the other $4$ randomly out of $39$. What are the chances you choose (some of) the correct $4$ out of $39$?