Question: A book has n typos. Two proofreaders, Prue and Frida, independently read the book. Prue catches each typo with probability p1 and misses it with probability q1 = 1 - p1, independently, and likewise for Frida, who has probabilities p2 of catching and q2 = 1 - p2 of missing each typo. Let X1 be the number of typos caught by Prue, X2 be the number caught by Frida, and X be the number caught by at least one of the two proofreaders.
(a) Find the distribution of X.
(b) For this part only, assume that p1 = p2. Find the conditional distribution of X1 given that X1 + X2 = t.