4.2 Multiplication Rules and Conditional Probability (4 points each) 1. There are 18 boys and 12 girls in Mrs. Pettit's 8th period Calculus class. If two people are chosen at random with replacement, find the probability that they both are girls. 2. A study has shown that 34% of people will be diagnosed with cancer in their lifetime. If you choose three people at random, what is the probability that two will be diagnosed with cancer, and one will not? 3. A bag of marbles contains 12 red marbles, 10 blue marbles, and 15 green marbles. If three marbles are drawn without replacement, find the probability of drawing two blue marbles and then one red marble. The following table represents a survey of students and their favorite classes. If one student is chosen, find the following probabilities. (4 points each). Freshmen So -homores 4. Find the probability that a student prefers history. 5. Find the probability that the student prefers history or math. 6. Find the probability that the student is a sophomore or prefers English. 7. Find the probability that the student prefers art, given that he or she is a junior