m118 Homework 8 (4.3) Name: Please work all problems and show your work. Remember, an answer with no justification is no answer. Based on concepts from Section 4.3 (More Conditional Probability - Use Trees AND Conditional Probability Formula for each problem) 1) A box contains 4 red markers and 2 blue markers. A marker is selected at random and its color is noted. If it is red it is replaced; otherwise it is not. A second marker is selected and its color is noted. If the second is blue, find the probability that the first was blue? 2) It is believed that 8% of the population has hepatitis. A medical firm has a new test to detect hepatitis. It was found that if a person has hepatitis, the test will detect it (show a positive result) in 96% of the cases; it was also found that it will still show a positive result in 3% of those who do not have hepatitis. What is the probability that a person who tests positive actually has hepatitis? 3) An unfair coin with Pr[H] = 0.55 is flipped. If the flip results in a head, one student is selected at random from a class of 4 girls and 6 boys. If the flip results in a tail, one student is selected from a different class containing 3 girls and 7 boys. Find the probability that the flip resulted in tails given that a boy was selected. 4) At a state university, 60% are undergraduates, 35% graduates and 5% are in special program. Also, 20% of the undergraduates, 40% of the graduates, and 70% of the special program students are local residents. If a student is selected at random and found to be a resident, find the probability that this student is not a graduate student. 5) Statistics shows that 6% of men are colorblind and 0.4% of women are colorblind. Assume that the population is half male and half female. Find the probability that the person selected is male given that they are colorblind? 6) At a small college, 60% of the students are women and women are twice as likely to take aerobics class. In one semester, 30% of women took the class. If a randomly selected student is found to have taken the aerobics class, what is the probability that this student is a woman? 7) One-half of the students on campus are females. Females are three times as likely to enjoy romantic comedies as men. Assume 60% of the women on campus enjoy romantic comedies. If a student is selected at random and is found to enjoy romantic comedies, what is the probability the student is a male