Question 1 (4 points) Find the indicated probability. Sammy and Sally each carry a bag containing a banana, a chocolate bar, and a licorice stick. Simultaneously, they take out a single food item and consume it. The possible pairs of food items that Sally and Sammy consumed are as follows. chocolate bar - chocolate bar licorice stick - chocolate bar banana - banana chocolate bar - licorice stick licorice stick - licorice stick chocolate bar - banana banana - licorice stick licorice stick - banana banana - chocolate bar Find the probability that at least one chocolate bar was eaten. [ J ,3, Question 10 (4 points) The following contingency table provides a joint frequency distribution for a group of retired people by age at retirement and career. Age at Retirement 50-55 56-60 61-65 Over 65 Total A1 A3 A4 Attorney 10 40 75 40 165 C1 Career College 5 30 80 60 175 Professor C2 Secretary 21 45 63 49 178 C3 Store Clerk 18 44 70 50 182 C4 Total 54 159 288 199 700 How many of these people were store clerks when they retired? A/Question 2 (4 points) Explain your answer. Which of the following could not possibly be a probability? A. -0.04 B. 10 C. O D. 0.20Question 3 (4 points) In a competition, two people will be selected from four finalists to receive the first and second prizes. The prize winners will be selected by drawing names from a hat. The names of the four finalists are Jim, George, Helen, and Maggie. The possible outcomes can be represented as follows. JG JH JM GJ GH GM HJHG HMMJ MGMH Here, for example, JG represents the outcome that Jim receives the first prize and George receives the second prize. The event A is defined as follows. A = event that Helen gets first prize Find the probability P(A). AThe number of hours needed by sixth grade students to complete a research project was recorded with the following results. Hours Number of students (f). 4 19 5 28 6 17 7 13 8 9 9 7 10+ 7 A student is selected at random. The event A is defined as follows. A = the event the student took between 5 and 9 hours inclusive Determine the number of outcomes that comprise the event (not A). A5 The number of hours needed by sixth grade students to complete a research project was recorded with the following results. m Number of students (if) 25 20 23 9 10 6 10+ 8 \\OGJNONUI-b A student is selected at random. The events A and B are defined as follows. A = the event the student took between 6 and 9 hours inclusive B = the event the student took at most 7 hours Determine the number of outcomes that comprise the event (A or B). A: students (if). 15 11 19 6 9 16 10 2 ~(30:27!\\IO'~t.J1.|:~. A student is selected at random. The events A and B are defined as follows. A = event the student took at most 6 hours B = event the student took at least 6 hours Are the events A and B mutually exclusive? - Determine whether the events are mutually exclusive and explain why or why not. The number of hours needed by sixth grade students to complete a research project was recorded with the following results. Number of students (f). 15 11 19 6 9 16 10 2 Hours \\OCDNQUIA A student is selected at random. The events A and B are defined as follows. A = event the student took at most 6 hours B = event the student took at least 6 hours Question 7 (4 points) A bag contains 4 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue? Answer maybe given as fraction or decimal. :l/ Question 8 (4 points) Find the indicated probability by using the special addition rule. The age distribution of students at a community college is given below. Age Number of (years). students (f). Under 21 419 21-25 405 26-30 204 31-35 60 Over 35 29 1117 A student from the community college is selected at random. Find the probability that the student is at least 31. Answer may be given as a fraction or round approximations to three decimal places. AQuestion 9 (4 points) Find the indicated probability by using the complementation rule. A relative frequency distribution is given below for the size of families in one U.S. city. Relative Size frequency. 2 0.442 3 0.241 4 0.195 5 0.075 6 0.031 7+ 0.016 A family is selected at random. Find the probability that the size of the family is at least 3. Round approximations to three decimal places. A/