Suppose Compositor A is preparing a manuscript to be published. Assume that she makes X errors on a given page, where X has the Poisson pdf, pX(k) = e−22k/k!, k = 0, 1, 2, . . . . A second compositor, B, is also working on the book. He makes Y errors on a page, where pY (k) = e−33k/k!, k = 0, 1, 2, . . . . Assume that Compositor A prepares the first one hundred pages of the text and Compositor B, the last one hundred pages. After the book is completed, reviewers (with too much time on their hands!) find that the text contains a total of 520 errors. Write a formula for the exact probability that fewer than half of the errors are due to Compositor A.