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Even’s

Even’s. 4.3 #60 Simpson’s Paradox. P(MA) = 490/700 = 70% P(FA) = 280/500 = 56% By school: P(MAB) = 480/600 = 80% P(FAB) = 180/200 = 90% P(MAL) = 10/100 = 10% P(FAB) =100/300 = 33.3% Because the %’s reversed, This IS Simpson’s Paradox. 4.3 #83 Simpson’s Paradox.

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Even’s

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  1. Even’s

  2. 4.3 #60 Simpson’s Paradox • P(MA) = 490/700 = 70% P(FA) = 280/500 = 56% • By school: • P(MAB) = 480/600 = 80% P(FAB) = 180/200 = 90% • P(MAL) = 10/100 = 10% P(FAB) =100/300 = 33.3% • Because the %’s reversed, This IS Simpson’s Paradox.

  3. 4.3 #83 Simpson’s Paradox • P(NSA)=502/732 =68.6% < P(SA)=443/582=76.1% • By Age: • P(NS18)=327/340=96.2% > P(S18)=269/288=93.4% • P(NS45)=147/199=73.9% > P(S45)=167/245=68.2% • P(NS65)=28/193=14.5% > P(S65)= 7/49 =14.3% • Because the %’s reversed, This IS Simpson’s Paradox.

  4. #30 • P(A)= person chosen completed 4+ college = 44845/175230 =.256 • P(B) = person is 55+ = 56008/175230 =.3196 • P(A and B) = 10596/175230 = .0605 • Are event A and B independent? • P(AnB) = P(A)*P(B)? P.351 • .0605 ≠ .256*.3196 so NOT ind.

  5. #36 • A) P(other) = .295 • B) P(Silver or White) = .176 + .172 = .348 • C) P(S or W) in 2 random selections = .348 X .348 = .121104

  6. #38 • P (A) is that the person chosen is Hispanic • P (B) is that the person chosen is White. • To be independent: • P(A)XP(B) must equal P(A and B) • .125 X .751 ≠ .060 Therefore they are not independent. (p 351)

  7. #40 P(portfolio goes up) = .65 • A) .653 = .275 • B) P( portfolio goes down) = .35 • C) P( moves in same direction both years) = P (up 2 years) + P ( down 2 years) so…… .652 + .352 = .545

  8. #42 • A) P(land in one slot) = 1/38 • B) P(winning red) = 18/38 • C) P(winning column) = 12/38

  9. #44 • P(1st child is albino) is ½ X ½ = ¼ • P(2 children are albino) = ¼ 2 = 1/16 • P(neither are albino) = ¾ X ¾ = 9/16

  10. Venn Diagrams and Notation

  11. #58 Poker Flush • P (1st card is spade) = 13/52 • P (2nd card is spade given that the first card was a spade) • = don’t make this hard= 12/51 • P (3rd spade) = 11/50 • P (4th spade) = 10/49 • P (5th spade) = 9/48 • P (Spades Flush) = .000495 • P (Dealt any Flush) = 4 x .000495 = .00198

  12. #59 Royal Flush • P( Royal Flush) would be • 5/52 x 4/51 x 3/50 x 2/49 x 1/48 • = .00000038447 for one suit • times 4 for any suit • Therefore .000001539 is the prob. Of getting a royal flush.

  13. Tree Diagrams

  14. #83 • P(FA used) = 18940/31510 = .601 • P(FA given F) = 2559/6095 = .420 • P(FA and F) = 2559/31510 = .081 • P(FA given M) = 16381/25415 = .645 • P(M given FA) = 16381/18940 = .865

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