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Name: _______________________________________________ Per: ____ Date: ______________Chapter 5 Problem Set A.P. Statistics1) A school’s debate club has 10 members, 6 females and 4 males. If the team decides to pick two members randomly to participate in a debate, what is the probability that both of the chosen members are female? We want to use simulation to estimate this probability. Describe the simulation procedure below, then use the random number table on the next page to carry out 10 trials of your simulation and estimate the probability. Mark on or above each line of the table so that someone can clearly follow your method. 141 96767 35964 23822 96012 94591 65194 50842 53372 142 72829 50232 97892 63408 77919 44575 24870 04178 143 88565 42628 17797 49376 61762 16953 88604 12724 144 62964 88145 83083 69453 46109 59505 69680 009002) Suppose you toss one coin and roll one six-sided die. (a) List the outcomes in the sample space. (b) Find the probability of getting a head. (c) Find the probability of getting a 1, 2, or 3 on the die. (d) Find the probability of getting a head or a five.3) In a statistics class there are 18 juniors and 10 seniors; 6 of the seniors are females, and 12 of the juniors are males. If a student is selected at random, find the probability of selecting (a) a junior or a female (b) not a junior male4) Consolidated Builders has bid on two large construction contracts. The company president believes that the probability of winning the first contract (event A) is 0.6, that the probability of winning a second (event B) is 0.3, and that the probability of winning both jobs is 0.1. (a) Construct either a Venn diagram or a two-way table that summarizes what you know about events A and B. (b) What is P (A or B) —the probability that Consolidated wins at least one of the job? (c) Write each of the following events in terms of A, B, Ac, and Bc, and use the information above to calculate the probability of each. i. Consolidated wins both jobs. ii. Consolidated wins the first job but not the secondiii. Either Consolidated does not win the first job or wins the second. iv. Consolidated does not win either job.5) The table below gives the counts (in thousands) of earned degrees in the United States in a recent year, classified by level and by the gender of the degree recipient. DegreeBachelor’sMaster’sProfessionalDoctoralTotalFemale6161943016856Male5291714426770Total114536574421626Suppose one degree recipient from this group is selected randomly. (a) List two mutually exclusive events for this chance process. (b) What is the probability that the person selected earned a Master’s degree? (c) What is the probability that the person selected earned a Professional or Doctoral degree? (d) What is the probability that the person selected is female or earned a Master’s degree? 6) Consider the following activity: The letters in the word AARDVARK are printed on identical plastic cards with one letter per card. The eight cards are then placed in a hat, and one card is randomly chosen (without looking) from the hat. The chance process we are interested in is what letter is on the selected card. (a) List the sample space S of all possible outcomes. (b) Make a table that shows the set of outcomes and the probability of each outcome: (c) Consider the following events: V: the letter chosen is a vowel. F: the letter chosen falls in the first half of the alphabet (that is, between A and M). List the outcomes in each of the following events, and determine their probabilities: V = { P(V) = F = { P(F) = V or F = { P(V or F) = Fc = { P(Fc) = V and F = { P(V and F) = V given F = { P(V|F) = (d) Are the events V and F are independent? Explain. (e) Are the events V and F mutually exclusive? Explain.7) Suppose a person was having two surgeries performed at the same time by different operating teams. Assume (unrealistically) that the two operations are independent. If the chances of success for surgery A are 85%, and the chances of success for surgery B are 90%, what is the probability that both will fail?8) Parking for students at Central High School is very limited, and those who arrive late have to park illegally and take their chances at getting a ticket. Joey has determined that the probability that he has to park illegally and that he gets a parking ticket is 0.07. He recorded data last year and found that because of his perpetual tardiness, the probability that he will have to park illegally is 0.25. Suppose that Joey arrived late once again this morning and had to park in a no-parking zone. Can you find the probability that Joey will get a parking ticket? If so, do it. If not, explain what additional information is needed in order to find the probability. 9) A frog is sitting exactly in the middle of a board that is five feet long. Every ten seconds he jumps one foot either left or right, at random. You want to use simulation to estimate the probability that he jumps off the board in sixty seconds or less. (For example, if he jumps LLRLRL, he is still on the board, on the left-most square. If he jumps LLRLL, he has jumped off the board in fifty seconds.) (a) Describe how you would use the digits of a random number table to simulate this chance process and estimate the probability. (b) Use the random number table below to carry out five repetitions of the frog’s jumps and give an estimate of the probability from those repetitions. 126 96927 19931 36089 74192 77567 88741 48409 41903 127 43909 99477 25330 64359 40085 16925 85117 36071 128 15689 14227 06565 14374 13352 49367 81982 87209 129 36759 58984 68288 22913 18638 54303 00795 08727 130 69051 64817 87174 09517 84534 06489 87201 97245 10) Your statistics class has 26 students in it—14 girls and 12 boys. Your teacher uses a calculator to select two students at random to solve a problem on the board. (a) What is the probability that both students are girls? (b) Given that the second student chosen is a girl, what is the probability that the first student was also a girl? 11) The table below gives the distribution of students at a certain high school for two categorical variables, grade year and the student’s answer to the question, “Do you eat regularly in the school cafeteria?” Grade9101112TotalsEat in cafeteria?YES13017512268495NO183488170310Totals148209210238805 a) If you choose a student at random, what is the probability he or she eats regularly in the cafeteria? b) If you choose a student at random, what is the probability he or she eats regularly in the cafeteria, given that he or she is in 10th grade? c) If you choose a student at random, are the events “10th grade” and “eats regularly in the cafeteria” independent? Explain how you know. ................
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