For this discussion, complete the following tasks: Write two linear equations with two variables that model something from your daily life. Solve the system of equations in two ways. Discuss which method you liked better and why.

 Is every 3-connected 3-regular, planar bipartite graph Hamiltonian?

INSTRUCTIONSInstructionsIf the question requires computation, do the calculations and then give or select the correct values using the following rule:Keep at least 4 decimal places at intermediate steps of a calculation, and round your final answer to 2 decimal places, unless otherwise noted. For example: 16.6667 would become 16.67 after rounding(In the course notes for Module 7, probabilities such .678934 are instead rounded to four decimal places, so the correct way to report the aforementioned probability is .6789Question 1Given the upcoming NBA (professional basketball) draft, there are several players available with skills at different positions (e.g., point guard) and with or without college experience. The table below summarizes these data. (Use the data below for this question only) College Experience (CE) No College Experience (NCE) Point Guard (PG) 29 27 Shooting Guard (SG) 19 29 Center (C) 37 10 Small Forward (SF) 19 39 Power Forward (PF) 16 13 Find the following probability: p(SG) (If necessary, round answer to 4 decimal places) Question 2Given the upcoming NBA (professional basketball) draft, there are several players available with skills at different positions (e.g., point guard) and with or without college experience. The table below summarizes these data. (Use the data below for this question only) College Experience (CE) No College Experience (NCE) Point Guard (PG) 24 29 Shooting Guard (SG) 17 21 Center (C) 13 14 Small Forward (SF) 20 17 Power Forward (PF) 27 37 Find the following probability: p(C and NCE) (If necessary, round answer to 4 decimal places) Question 3Given the upcoming NBA (professional basketball) draft, there are several players available with skills at different positions (e.g., point guard) and with or without college experience. The table below summarizes these data. (Use the data below for this question only) College Experience (CE) No College Experience (NCE) Point Guard (PG) 24 19 Shooting Guard (SG) 24 30 Center (C) 30 25 Small Forward (SF) 14 24 Power Forward (PF) 11 33 Find the following probability: p(CE) (If necessary, round answer to 4 decimal places) Question 4Given the upcoming NBA (professional basketball) draft, there are several players available with skills at different positions (e.g., point guard) and with or without college experience. The table below summarizes these data. (Use the data below for this question only) College Experience (CE) No College Experience (NCE) Point Guard (PG) 16 38 Shooting Guard (SG) 11 38 Center (C) 29 10 Small Forward (SF) 31 35 Power Forward (PF) 20 35 Find the following probability: p(not C) (If necessary, round answer to 4 decimal places) Question 5Given the upcoming NBA (professional basketball) draft, there are several players available with skills at different positions (e.g., point guard) and with or without college experience. The table below summarizes these data. (Use the data below for this question only) College Experience (CE) No College Experience (NCE) Point Guard (PG) 20 15 Shooting Guard (SG) 27 33 Center (C) 11 15 Small Forward (SF) 20 33 Power Forward (PF) 23 30 Find the following probability: p(CE/PG) (If necessary, round answer to 4 decimal places) Question 6Given the upcoming NBA (professional basketball) draft, there are several players available with skills at different positions (e.g., point guard) and with or without college experience. The table below summarizes these data. (Use the data below for this question only) College Experience (CE) No College Experience (NCE) Point Guard (PG) 38 34 Shooting Guard (SG) 23 31 Center (C) 16 36 Small Forward (SF) 36 29 Power Forward (PF) 18 35 Find the following probability: p(PG/CE) (If necessary, round answer to 4 decimal places) Question 7Randomly sample one person from a population of 100 people: 50 children, 20 teens, and 30 adults. What is the probability that your selectee is a child OR an adult? (Leave your answer in probability decimal form with 2 decimal places; do not convert to a percentage.)Question 8A stable has all American Quarter Horses. There are 21 bays, 10 blacks, and 8 red duns. (Use these data for this question only.) What is the probability that you randomly select a black, don’t put the black back, then draw another black, don’t put that black back, and then draw another black quarter horse? (If necessary, round answer to 4 decimal places)Question 9A stable has all American Quarter Horses. There are 24 bays, 11 blacks, and 11 red duns. (Use these data for this question only.) What is the probability that you draw a bay or a red dun on the first draw, replace that horse, and then draw a black horse? (If necessary, round answer to 4 decimal placesQuestion 10A stable has all American Quarter Horses. There are 20 bays, 13 blacks, and 7 red duns. (Use these data for this question only.) What is the probability that you draw a red dun on the first draw, don’t put the red dun back, and then draw either a red dun or a bay on the second draw? (If necessary, round answer to 4 decimal places) Question 11Theresa has many ICU patients in her care. Some of the patients are on feeding tubes while others are on IVs only. In addition, Theresa knows that some of the patients have diabetes while some don’t. The exact breakdown is as follows: (Use these data for this question only.) Feeding Tube IV Has Diabetes 67 69 No Diabetes 8 27 What is the probability of selecting someone who does not have diabetes, given that they are on a feeding tube? (If necessary, round answer to 4 decimal places)Question 12Theresa has many ICU patients in her care. Some of the patients are on feeding tubes while others are on IVs only. In addition, Theresa knows that some of the patients have diabetes while some don’t. The exact breakdown is as follows: (Use these data for this question only.) Feeding Tube IVHas Diabetes 74 30No Diabetes 7 20What is the probability of selecting someone who has diabetes and on an IV?(If necessary, round answer to 4 decimal places)Question 13Theresa has many ICU patients in her care. Some of the patients are on feeding tubes while others are on IVs only. In addition, Theresa knows that some of the patients have diabetes while some don’t. The exact breakdown is as follows: (Use these data for this question only.) Feeding Tube IV Has Diabetes 65 48 No Diabetes 10 34 What is the probability of selecting someone who is on an IV, given that they do not have diabetes? (If necessary, round answer to 4 decimal places)Question 14A six-sided die is rolled 3 times. Which outcome is most likely?1-2-33-5-25-5-5All are equally likelyNone of the aboveQuestion 15Which of the following is not a valid way to express a probability?2/314/17.9-0.1All are validQuestion 16The gambler’s fallacy applies toIndependent eventsCategorical variablesMutually exclusive eventsFalse positivesQuestion 17An exhaustive set of events isA set of events that do not depend on the outcome of other events.A list of the most likely outcomes.A list of all possibilities.A set of events that are not mutually exclusive.something that leaves you fatigued and in need of extra sleep ; -)Question 18Which of the following is an example of the subjective view of probability?By reviewing insurance paperwork of all patients, a hospital administrator determined that coding errors are made 13% of the time.By reviewing insurance paperwork of a random sample of patients, a hospital administrator determined that coding errors are made 8% of the time.By remembering his experiences dealing with insurance errors, a hospital administrator determined that coding errors are made 20% of the time.Question 19A student guesses randomly on four true/false questions on an exam. What is the probability that all answers are correct?0.0625.3333.51Question 20Which of the following is not an example of independent events?A student guesses randomly on 6 exam questions.A gambler rolls a pair of dice three times.Four cards are drawn from a deck, with replacement.Three cards are drawn from a deck, without replacement.