PRACTICE EXAM PART 1 Section 4.1-4.5 Problem 1. a) Given the event A: Rolling a die twice. Write the sample space of event A b) Given the event B: A couple having 4 children. Write the sample space of all possible sequences of genders for event B. Find the probability of having exactly one boy d) Find the probability of having exactly two boys e) Find the probability of having exactly three boys A Find the probability of having no boys g) Find the probability of having at least one boys Problem 2. About 35% of the population has blue eyes (based on a study by Dr. P. Sorita Soni at Indiana University). a) If someone is randomly selected, what is the probability that he or she does not have blue eyes? b) If four different people are randomly selected, what is the probability that they all have blue eyes? Q-----o-----o Problem 3. The first complement rule: If P(Ā) = 0.32 then P ( A) Problem 4. In a drawer, there are 15 blue socks, 4 green socks and 10 whice sucks. If Maria draws 1 sock at random, a) What is the probability that the sock he draws will be blue? b) What is the probability that the sock he draws will be white? c) Find P (blue or green) d) Find P ( white) e) Find P ( white ) Problem 5. There are 19 red socks, 7 green socks and 3 blue socks in a drawer. a) Randomly select 2 socks Find the probability that the first selected sock is red; the second selected sock is blue, with replacement b) Randomly select 2 socks. Find the probability that the first selected sock is red; the second selected sock is blue, without replacement c) Randomly select 3 socks .Find the probability that the first two are red; and the last one is green. Without replacement d) Randomly select 2 socks. Find the probability that there are one red and one blue; without replacement Problem 6. Use the data in the accompanying table. (based on data from “Helmet Use and Risk of Head Injuries in Alpine Skiers and Snowboarders") Head Injuries Not Injured 96 480 Wore Helmet 656 No Helmet 2330 a. Helmets and Injuries If one of the subjects is randomly selected, find the probability of selecting someone with a head injury. b. Helmets and Injuries If one of the subjects is randomly selected, find the probability of selecting someone who wore a helmet. c. Helmets and Injuries If one of the subjects is randomly selected, find the probability of selecting someone who had a head injury or wore a helmet. d. Helmets and Injuries If one of the subjects is randomly selected, find the probability of selecting someone who did not wear a helmet and was not injured. e. Helmets and Injuries If two different study subjects are randomly selected, find the probability that they both wore helmets, without replacement f. Helmets and Injuries If two different study subjects are randomly selected, find the probability that they both had head injuries, without replacement g. Helmets and Injuries If one of the subjects is randomly selected, find the probability of selecting someone who did not wear a helmet, given that the subject had head injuries. h. Helmets and Injuries If one of the subjects is randomly selected, find the probability of selecting someone who had head injuries, given that the subject wore helmet. Problem 7. (5 points) A IRS auditor randomly selects some tax returns from 59 returns of which 9 contain errors. a) What is the probability that when selecting 3 tax retums, none of those containing errors? b) What is the probability that when selecting 3 tax returns, at least one of those containing errors?