FINITE MATHEMATICS FOR THE SOCIAL AND MANAGEMENT SCIENCES Department of Mathematics, George Washington University Math 1051 Fall 2022 HOMEWORK 4 DUE November 21, at the beginning of the Lecture 1. Of the 9digit passwords formed from 1 to 9, allowing repeats, I select one at random. Determine the following probabilities: (a) Prob (my word is 2 573000000) (b) Prob (my word includes exactly one even digit) 5 points ((3) Prob (my word begins or ends with an even digit) ((1) Prob (my word includes at most two even digits and is a palindrome) Leave your probabilities in terms of m" and P771". 2. Of the 9letter passwords formed from A to Z, without repeats, I select one at random. Deter mine the following probabilities: (a) Prob (my word includes at most one vowel) (b) Prob (my word begins and ends with a vowel) 5 points (c) Prob (my word begins with A and includes exactly one other vowel) (d) Prob (my word includes exactly two vowels and they are not beside each other) Leave your probabilities in terms of m\" and Pg\". The vowels are A, E, I, O, and U