Hi please use the given information to answer each part of the problem and please include any drawing, or steps/formulas to improve my understanding of the problem if necessary. Thank you! Please do not repost response from other post.

Of the 100 people in a village, 50 always tell the truth, 30 always lie, and 20 always refuse to answer. A sample of 30 people is drawn with replacement. Let N1 be the number of truth-tellers in the sample and N2 be the number of liars (so the number who refuse to answer is 30 N1 N2. (a) Find the joint pmf of N1, N2. (b) Find the marginal pmf of N1. (0) Find the conditional pmf of N2 given N1 = 10. Remark: The joint pmf above is an example of a multinomial pmf, which generalizes binomial pmf to more than two partitions