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MAT 142 Summer Session 1 ANSWERS Homework Day #12: Name:______________________ I. Odds Navigate to http://en.wikipedia.org/wiki/Odds to read a little more about the topic of Odds that we discussed today in class. 1. A.M. (initial that you read the article) Note: they use a slightly different formula than the one we wrote in our notes BUT it works out to be the same thing right? 2. A die is tossed. Determine the odds against rolling a number greater than 4. “ 4 to 2” or “ 2 to 1” A card is picked from a standard deck of cards. Determine the odds against AND the odds in favor of selecting…. 3. A King odds against = 12:1 odds for = 1:12 odds against = 3:1 odds for = 1:3 4. A Diamond In a certain math class there are 24 female students and 6 male students. If one person is selected at random from this class determine the odds against selecting…. 5. A female 1:4 Note: since there are 4 times as many females as males these answers should make sense to you right? 6. A male 4:1 The following table shows, among other things, the winnings in dollars for the top 10 rated NASCAR drivers (according to points standings) for the 2005 season. RANK +/- DRIVER POINTS BEHIND STARTS POLES WINS TOP 5 TOP 10 WINNINGS 1 -- Tony Stewart 6533 Leader 36 3 5 17 25 6,987,530 2 +2 Greg Biffle 6498 -35 36 0 6 15 21 5,729,930 3 -- Carl Edwards 6498 -35 36 2 4 13 18 4,889,990 4 +1 Mark Martin 6428 -105 36 0 1 12 19 5,994,350 5 -3 Jimmie Johnson 6406 -127 36 1 4 13 22 6,796,660 6 -- Ryan Newman 6359 -174 36 8 1 8 16 5,578,110 7 -- Matt Kenseth 6352 -181 36 2 1 12 17 5,790,770 8 -- Rusty Wallace 6140 -393 36 0 0 8 17 4,868,980 9 +1 Jeremy Mayfield 6073 -460 36 0 1 4 9 4,566,910 10 -1 Kurt Busch 5974 -559 34 0 3 9 18 6,516,320 7. If one driver in this list is selected at random what is the probability that the driver earned more than $6 million in 3 2005? 10 8. What are the odds against the driver earning more than $6 million in 2005? 7:3 9. The odds against earning a C or better in MAT142 are said to be 4:11. Determine the probability of a random student earning a C or better in MAT142. 11 15 II. Tree Diagrams Two coins are tossed. 11. Use the counting principle to determine the number of points in the sample space. 2 x 2 =4 12. Construct a tree diagram and list the sample space. Sample Space H HH H T HT T H T TH TT 13. Determine the probability that A) No head is tossed 1 4 B) exactly one head is tossed C) two heads are tossed 1 2 Two dice are rolled. 14. Use the counting principle to determine the number of points in the sample space. 6 x 6 = 36 1 4 15. Construct a tree diagram and list the sample space. 1 2 3 4 5 6 Sample Space 11 12 13 14 15 16 1 2 3 4 5 6 1 2 3 4 5 6 21 22 23 24 25 26 1 2 3 4 5 6 31 32 33 34 35 36 1 2 3 4 5 6 41 42 43 44 45 46 1 2 3 4 5 6 51 52 53 54 55 56 1 2 3 4 5 6 61 62 63 64 65 66 16. Determine the probability that.. A) a double is rolled (i.e a 1,1 or a 2,2 etc.) 1 6 B) A sum of 7 is rolled 1 6 C) a sum of 2 is rolled 1 36 17. Navigate to http://regentsprep.org/Regents/Math/counting/PracCnt.htm and try the five problems using the Counting Principle! Write down your answers to the five problems. Be sure to try the problems yourself BEFORE you look at the explanation (and answer). 1. 9 2. 75 3. 676,000 4. 930 5. 24 18. If two states are selected at random from the 50 U.S. states, use the counting principle to determine the number of possible outcomes if the states are selected… A) without replacement 50 x 49 = 2450 B) with replacement 50 x 50 = 2500 Do you need (want) extra practice? Go to http://www.worksheetworks.com/math/probability/countingprinciple.html and click on the “create worksheet” button at the bottom of the web page. Click on the pdf link and a worksheet with more practice problems (followed by an answer key) will be generated.