Anew law proposal is submitted to the parliament of a country. There are n members of the government party, who will all certainly vote in favor of the proposal, m members of the leading opposition party who will all vote against the proposal, while there are also k parliament members who belong to other parties; we assume that m < n, k < n, but m + k > n. In the last group of k parliament members, each person will vote in favor of the proposal with a probability p, and against it with a probability q = 1 − p, and we assume that they reach a decision independently of one another.

(i) Find the probability function for the number X of votes that will be cast in favor of the law proposal.

(ii) Find the probability that the proposal is approved by the parliament.