MAT 114 Assignment Two Note that this assignment has two deadlines. Problem 1 is a discussion item and your response should be posted as such. Problem 2 should be answered in a single document as an Assignment. 1. Discussion regarding the FDA (3 points) You are asked to read the two or three articles linked in the paragraph below and then to post a Discussion thread on Bb Learn. Your first posting will be blind - you will not be able to see what anyone else is thinking. You are then asked to read the posts of others and submit a second post that references at least one post from another learner. (It is likely that someone will mention something you had not thought of and will add to your understanding of the FDA. Do mention the name of the student(s) whose postings added such value to you.) Your first post is worth 1 point; the second is worth up to 2 points. The Food and Drug Administration takes a very careful approach to its approval of new drugs before they are approved for use: http://www.fda.gov/drugs/developmentapprovalprocess/default.htm. However sometimes the FDA gives the go-ahead to a drug which is later found to be unsafe and is withdrawn from the market. A well known case involves the Cox-2 inhibitor VIOXX - see for example http://www.fda.gov/Safety/MedWatch/SafetyInformation/SafetyAlertsforHumanMedicalProducts/ ucm166532.htm and http://en.wikipedia.org/wiki/Rofecoxib which was approved by the FDA in 1999 and withdrawn in 2004. Given that the FDA is so careful, why do such mistakes happen? Is it bad science, bad statistics or simple bad luck? Maybe some of each? Or something else? Discuss in the context of Units One and Two. As an aside there is now (since 2013) some concern at the use of ibuprofen - Advil, Motrin, Excedrin etc. See for example http://www.forbes.com/sites/johnlamattina/2013/06/01/the-fdas-dilemma-aboutibuprofen-and-cardiovascular-risk/ and http://www.nlm.nih.gov/medlineplus/druginfo/meds/a682159.html . The first article states that ibuprofen may be equally hazardous as VIOXX. You are welcome to mention this in your discussion posting. 2. Your best bet (6 points) Submit your work as an Assignment. In this problem you are asked to carry out two expected value calculations on real world gambling games and to compare them with information provided on a third. Consider a game of roulette in which a wheel is spun so that a ball lands randomly in one of 38 numbers. A roulette wheel has 38 numbers, labeled 1-36 plus the special numbers 0 and 00 for which all gamblers lose to the house. The picture below shows which numbers correspond to red. Picture from: http://www.roulettebet.net/images/roulette-table.gif A a) What is the probability of getting a black? b) What is the probability of NOT getting a black? c) Given that a gambler choosing black wins $1 if black occurs and loses $1 if black does not occur, what is the expected value for a single $1 play of this game? B a) What is the probability of getting a specific number - say the number 17? b) What is the probability of NOT getting that number? c) Given that a gambler choosing 17 wins $34 if 17 occurs and loses $1 if 17 does not occur, what is the expected value for a single $1 play of this game? 3. Keno (6 points) In Keno, a player chooses 20 numbers from a list of 80. Each gamble costs $1. The table below shows the probability of getting anything from 0 up to all 20 correct together with the casino's posted winning amounts. [Note that 17-or-more numbers correct pays out $20,000. Not bad for a $1 bet! But note that the probability of doing so is incredibly small; the bottom number in the table may be the smallest number that you have ever seen!!] a) Note that the table shows that getting 3-6 numbers correct pays nothing. What is the probability of winning a payout of nothing (and therefore losing $1)? b) What is the probability of winning a payout of exactly $1 (and therefore getting your $1 bet back)? c) Compute the expected return on a $1 bet using the information in the table. There are a lot of numbers, but the calculation really isn't too bad. Don't let the size of the table intimidate you! Then subtract the $1 bet to find the expected winnings. Number correct 0 Probability 0.00118570600000000000 Winnings (dollars) 200 1 0.01156786100000000000 2.40 2 0.04971425800000000000 1 3 0.12486371700000000000 0 4 0.20503189900000000000 0 5 0.23328073800000000000 0 6 0.19017451500000000000 0 7 0.11329545600000000000 1 8 0.04986180200000000000 2 9 0.01628140500000000000 5 10 0.00394010000000000000 10 11 0.00070233500000000000 40 12 0.00009116850000000000 200 13 0.00000846848000000000 1000 14 0.00000054888300000000 2500 15 0.00000002395130000000 5000 16 0.00000000066828300000 10000 17 0.00000000001103460000 20000 18 0.00000000000009512590 20000 19 0.00000000000000033943 20000 20 0.00000000000000000028 20000 4. Your Best Bet Casinos advertise a 95% payback for their slot machines. This means that for a $1 stake, a gambler can expect to get 95 cents back. a) What does 95% payback mean in terms of the expected value of a play on the slot machines? i.e. What is the expected value of a pull on the slots? b) How does this compare to choosing 'black' or '17' on roulette or playing Keno? Which is the best bet? Grading Rubric for the Assignment Assignment turned in on time [1] Paper turned in up to one day late [0] The paper will not be accepted more than one day late. [1] Problem 1. Discussion [3] Problem 2A a, b Problem 2A c Problem 2B a, b Problem 2B c Correct computation of probabilities Correct computation of the expected value Correct computation of probabilities Correct computation of the expected value [] [1] [] [1] Problem #3 a, b Problem #3 c Correct computation of probabilities Correct computation of the expected value [1] [1] Problem #4 a Problem #4 b Correct interpretation of expected value Correct comparison/interpretation of the four games [1] [1] One point of extra credit is available on this assignment