MAT 121 WEEK 6 NOTES!
MAT 121 WEEK 6 NOTES! MAT 121
Popular in Probability and Statistics for the Liberal Arts I
Popular in Mathematics (M)
This 11 page Class Notes was uploaded by Aria Sivick on Friday October 9, 2015. The Class Notes belongs to MAT 121 at Syracuse University taught by in Fall 2015. Since its upload, it has received 52 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: 10/09/15
105 Toss coin until HEADS and observe the number of tosses An urn has 7 red balls and 4 green ones Pick 2 balls PReds 7 ll6 10 7ll35 Def PAB the conditional probability of 4 assuming that B has happened probability of A given B When PA PAB the events A and B are said to be independent Pred 1st and red 2nd Pred lst Pred 2nd red lst General Multiplication Rule PA and B PA PBA PB PAB Special Multiplication Rule If A and B are independent then PA and B PA PB Sampling with replacement independence Sampling Without replacement don t have independence exception When we sample from a very large population its convenient to assume independence Pwomen 1st 169922150 368 521 785 Pwomen 2nd 169 922150 338 521 784 EX 102 out of 810 scales are defective Pick 2 and ask Pboth defective 1 With replacement Pboth defective Plst defective m 2nd defective Plst defective P2nd defective m X amp 016 8 10 8 10 2 Without replacement not independent Pboth defective Plst defective and 2nd defective P 1 st defective X P2nd defective lst defective amp X 0157 810 809 EX Urn 15 red 20 green Take 2 Without replacement Pthe second one Will be the green Pred lst and green 2nd green lst and green 2nd Pred lst and green 2nd P green lst and green 2nd 342034 471934 m t 238 7 PDifferent colors Pred then green or green then red Pred lst and green 2nd P green lst and red 2nd 107 Choose of those 1000 persons at random 0005i V 465w Ek C 5 t AA a u if i lt Events M person is male W M bar person is female C person prefers Coke P C bar person prefers Pepsi 1 PC 61C 6 1000 2 What s the probability that the chosen person is a woman Who prefers Pepsi W P PW and P 200 2 1000 3 When is the probability of choosing a woman or a coke preferer PW or C 350 250 800 8 1000 1000 1000 4 What s PCW If the person chosen is a woman what s the probability that she prefers Coke If one of the women is chosen at random what s the probability that one prefers Coke What proportion of the women prefer Coke Answer 5 5 556 400 9 PCW PC and W 2501000 25 556 PW 450 1000 450 5 Are gender and cola preference independent PCW 556 No because PC is not equal to PCW PC 600 The following are equivalent 1 A and B are independent 2 PA PAB PA B bar 3 PA and B PA PB 109 0 O i Q CA C mowoms lmrce mum on mac Mamet3M NUS vcm CMd JCM Q QCA N v79 130 MED PCA om 3 I 5 QCA mm 3 0 CA Oma 3 M c muyuuwauuus wo LVWCA cm vsgtvm x CBA A and 3 N6 M eecn cjgi t W o wa H H PCAY A A3 E mm O lth Qm quot gf ghx pCA mm 3gt CA 03 i 39 z 73 awe enxa In 39 gis W 7 Mmenka U diWnk has MD M 3wucae meow amm PMS W7xodut 1 gw daw 03930 mgw ws A Asw 6MB Wm OLbK can boob16 n n 008 500 an oc Ame A norm nk Mama Men W M 0 9 EMMA wages cm 1 o g 7 swam 7 O r Tynan Mama 3046 cam ioaw vwm naz Am 70344324 50Ho A CD Fb waao mer examme 50142 L HEM 3 PYOK Cm A80 A06 BAG BCA 161 a Uquot 9 33U3gtC7 Lu L163 moowvzax 5 t We a quot p t 7 2 0 7 1 O