MAT 121 WEEK 7/ EXAM REVIEW NOTES
MAT 121 WEEK 7/ EXAM REVIEW NOTES MAT 121
Popular in Probability and Statistics for the Liberal Arts I
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This 7 page Class Notes was uploaded by Aria Sivick on Saturday October 17, 2015. The Class Notes belongs to MAT 121 at Syracuse University taught by in Fall 2015. Since its upload, it has received 203 views. For similar materials see Probability and Statistics for the Liberal Arts I in Mathematics (M) at Syracuse University.
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Date Created: 10/17/15
1012 Multiplication Principle n n factorialquot n n ln 2 2l the number of ways to order 11 things Q In how many ways can I choose and order 7 of 10 things Pick the lst 10 ways Pick the 2nd 9 ways Pick the 7th 4 ways Ans lOX9X8X7X6X5X46O4800 Q In how many ways can I choose and order r things from 11 things Pick the lst 11 ways Pick the 2nd n l ways Pick the 3rd n 2 ways Pick the rth way n rl ways Ans nn ln 2 n rl nn ln 2 n rl 32l n rn rl 32l L IIr nPr n39 nn l n lr the number of permutations of r things chosen from 11 thingsquot How many 3 character passwords can be made from ABCD if repeated letters are not allowed Ans 4P3 choose and order 3 of the 4 things 4X3X2Xl 24 4 3 1 1 ABC ABD ACD BCD ACB ADB ADC BDC BAC BAD CAD CBD There are only 4 ways to pick 3 of the 4 things CAB BDA DAC DBC CBA DAB DCA DCB 24 6 In how many ways can I choose r things from 11 things m nPr counts each choice of r things r times So nPr counts each choice of r things once r nCr n nn ln rl n rr rr ll the number pf combinations of r things chosen from 11 things Combinations different orders are counted as one Permutations each different order counted separately 30 kids in class including Bobby 1 Teacher randomly picks 3 for ice cream What s the PBobby gets ice cream 30X29X28 321 There are 30C3 4060 equally likely choices of 3 students 29x28 29X14 406 2X1 Of these 29C2 include Bobby Answer 406 1 4060 2 Teacher randomly picks president Vice president secretary What s the PBobby is Vice president 30X29X28 There are 30P3 24360 equally likely choices of class of cers 29x28 812 29P2 29P2 of those have Booby as VP Answer 810 033 24360 34 male 39 female Pick 3 at random a Pall females 9139 147 62196 b Pat least 1 female a 73X72X71 62196 6 73X72X71 3X2X1 There are 73C3 62196 equally likely chances of of 3 students of them 73C3 9139 have all females b 1 Pall male 1 34C3 1 5984 904 62 196 62196 1014 30 people at party Assume 366 equally likely birthdays Fatica bets 10 that 2 people share birthday Adam bets 10 that the 30 bdays are different PFatica Wins Pduplicate bday l Pbdays all different l 366366365366364366363366 337366 705 l prodseq X366 X 337 366 21 people at party born randomly in June 20 b days in June Pmatch l Pall different l 303029302830lO30 999 Note The C is used When there is no order The P is used When there is order gtkOn the exam P s Will most likely not be used A city council has 7 Democrats and 4 Republicans They randomly pick 4 of their group to attend a convention of city council persons What s the probability that 1 Both political parties are represented 919 2 There s at least one Republican 929 3 2 Democrats 2 Republicans 424 m 495 There are 12C4 equally likely choices of the 4 person delegation 2 There are 7C4 35 With all Democarats there are 5C4 With all Republicans l l2XlleOX9 495 or 12C4 12 4X3X2Xl l2X4 4 There are 12C4 equally likely choices of the 4 person delegation 3 of these 7C2 X 5C2 have 2 Dems and 2 Republicans 21XlO 210 E X 21X10210 2X1 2X1 nCr a binomial coef cient Things on the test empirical rule 2 scores probability question contingency table various questions of that probability are they dependent independent counting problem too 4 question test 1015 Review List for Next Exam 1 De nitions and Formula 2 P 103 Empirical Rule 3 P 104 Figure 3 3 4 P 112 Z scores 5 P113 Unusual value farther from O 6 P 151 Additional Rule 7 P157 Multiplication 8 P168 The probability of at least one a Pat least one 1 Pnone b 2 8
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