MATH 1600-Assignment 4 Due: February 22, 2024 1. There are 18 girls and 12 boys in a class. Two-ninth of the girls and 1/4 of the boys walk to school. One of the students who walks to school is chosen at random. Find the probability that the student is a boy. (4pts.) 2. Rachel flips a biased coin. The probability that she gets two heads is 0.16. What is the probability that she gets two tails? (4 pts.) 3. There are 12 marbles in a bag. There are n red marbles and the rest are blue marbles. Nico takes 2 marbles from the bag. Write an expression involving n for the probability that Nico takes one red marble and one blue marble. (3 pts.) 4. Alice has some red balls and some black balls in a bag. Altogether she has 25 balls. Alice picks one ball from the bag. The probability that Alice picks a red ball is x and the probability that Alice picks a black ball is 4x. Work out how many black balls are in the bag. (3 pts.) 5. A problem is given to three persons P, Q, R whose respective chances of solving it are 2/7, 4/7, 4/9 respectively. What is the probability that the problem is solved? (4 pts.) 6. Volunteers for a disaster relief effort were classified according to both specialty (C: construction, E: education, M: medicine) and language ability (S: speaks a single language fluently, T: speaks two or more languages fluently). The results are shown in the following two-way classification table: Language Ability Specialty S T C 12 1 E 4 3 M 6 2 A volunteer is selected at random, meaning that each one has an equal chance of being chosen. Determine each of the following probabilities. (6 pts.) a) The probability that his specialty is medicine and he speaks two or more languages; b) The probability that either his specialty is medicine or he speaks two or more languages; c) The probability that his specialty is something other than medicine.