Psychology 2810-650 Unit 3: Probability I Assignment 3 1. 2. 3. If a student in a statistics course gets an average score of 75% on a number of quizzes, the probability that she will get an A on the midterm is .80. Based on the quiz scores she has received so far, the probability that she will not achieve a 75% average is .15. Also, the probability that she will not get an A on the midterm given that she fails to achieve a 75% average on quizzes is .70. a) What is the probability that the student will achieve a 75% average on quizzes and will get an A on the midterm? b) What is the probability that the student will not achieve a 75% average on quizzes and will get an A on the midterm? c) What is the probability that the student will not achieve a 75% average on quizzes or will get an A on the midterm? d) Are the events that a student achieves a 75% average on quizzes and the event that she gets an A on the midterm independent or dependent? Show how you arrive at your answer. Tom, Dick, and Harry often play tennis together. Tom usually wins: in fact, he has beaten Dick in 6 out of the last 10 games they've played together, and has only lost 3 of the last 12 games he's played with Harry. One day, all three are at the tennis courts and Dick and Harry toss a fair coin to decide which one will play Tom. a) What is the probability that Tom will win the game? b) Suppose Tom were to win. What would the probability have been that he played Harry? The probability that a rare tropical disease will be diagnosed correctly is .70. If it is diagnosed correctly, the probability is .90 that it can be cured. If it is not diagnosed correctly, the probability is .40 that it can be cured. If a patient having this disease were to be cured, what would the probability have been that the disease was diagnosed correctly? 4. People who have been exposed to a particular virus have a .95 probability of contracting a fatal disease. 80% of the people who have not been exposed to the virus will not contract the disease. If a doctor sees 200 patients, of whom 130 have been exposed to the virus, then: a) What is the probability that any randomly selected patient from these 200 will contract the disease? b) If, at some point in the future, one of these 200 patients were to contract the disease, what would the probability have been that he or she had been exposed to the virus? Answers: 1. a) .68 b) .045 c) .83 d) dependent 2. a) .675 b) .556 3. .84 4. a) .6875 b) .898