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Trisaba

  • one year ago

the principal of a school plans a school picnic for June 2. a few days before the event, the weather forecast predicts rain for June 2, so the principle decides to cancel the picnic. consider the following information. in the school's town, the probability that it rains on any day in June is 3%. when it rains, the forecast correctly predicts rain 90% of the time. when it does not rain, the forecast incorrectly predicts rain 5% of the time. let event a be the event that it rains on a day in June. let event b be the event that the forecast predicts rain. do you think the principal...

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  1. Trisaba
    • one year ago
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    made a good decision? why or why not?

  2. Trisaba
    • one year ago
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    this is a series of questions

  3. Trisaba
    • one year ago
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    @dan815

  4. Trisaba
    • one year ago
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    what is probability of b given a

  5. Trisaba
    • one year ago
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    P(B l A)

  6. dan815
    • one year ago
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    okay what is B and A

  7. Trisaba
    • one year ago
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    in the question

  8. Trisaba
    • one year ago
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    last two lines

  9. dan815
    • one year ago
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    P(B|A) means A given B or B given A?

  10. Trisaba
    • one year ago
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    b given a

  11. dan815
    • one year ago
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    okay so chance the forecast predicts right given it rains then

  12. dan815
    • one year ago
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    when it rains, the forecast correctly predicts rain 90% of the time.

  13. dan815
    • one year ago
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    P(B|A)=0.9=90%

  14. Trisaba
    • one year ago
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    a formula for P(B l A) is that is P(A intersection B) times P(A) all divided by P(B)

  15. Trisaba
    • one year ago
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    ?

  16. Trisaba
    • one year ago
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    no not times P(A) formula above

  17. Trisaba
    • one year ago
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    how did you figure out that the second thing was that

  18. dan815
    • one year ago
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    P(B|A)=P(a n b)/P(b) like that?

  19. Trisaba
    • one year ago
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    yeah

  20. dan815
    • one year ago
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    because the statement is already telling us what we want

  21. Trisaba
    • one year ago
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    no

  22. Trisaba
    • one year ago
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    P(A) at bottom

  23. Trisaba
    • one year ago
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    how did you know it was it

  24. dan815
    • one year ago
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    oh sry ya p(a) bottom

  25. dan815
    • one year ago
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    P(B|A) is asking the probability of B given A probability of rain prediction when it rains

  26. dan815
    • one year ago
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    and this statement is giving you the answer "when it rains, the forecast correctly predicts rain 90% of the time. "

  27. Trisaba
    • one year ago
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    oh

  28. Trisaba
    • one year ago
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    now what is P(A)

  29. Trisaba
    • one year ago
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    now what is P(A)

  30. dan815
    • one year ago
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    3% chance it rains on a day in june

  31. Trisaba
    • one year ago
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    is a?

  32. dan815
    • one year ago
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    ya

  33. Trisaba
    • one year ago
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    \[P \left( a ^{c} \right)\] is what

  34. Trisaba
    • one year ago
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    .97?

  35. dan815
    • one year ago
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    |dw:1441061445919:dw|

  36. dan815
    • one year ago
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    or100%-3%= 1-0.03

  37. dan815
    • one year ago
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    yes compliment raining is not raining, which is 97%

  38. Trisaba
    • one year ago
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    P(B l A complement) is?

  39. dan815
    • one year ago
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    that means chance of prediction when there is no rain

  40. dan815
    • one year ago
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    |dw:1441061765626:dw|

  41. Trisaba
    • one year ago
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    5%?

  42. dan815
    • one year ago
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    yeah

  43. Trisaba
    • one year ago
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    \[P(A) \times P(B l A) + P(A ^{c}) \times P(B l A ^{c})=P(B)\]

  44. Trisaba
    • one year ago
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    |dw:1441062094509:dw|

  45. Trisaba
    • one year ago
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    a complement we said was .97

  46. dan815
    • one year ago
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    yeah

  47. Trisaba
    • one year ago
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    so what are the question marks

  48. dan815
    • one year ago
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    when it does not rain, the forecast predits 95% of the time it wont rain and 5% it will rain

  49. dan815
    • one year ago
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    that what it means by 5% wrong prediction when it does not rain

  50. dan815
    • one year ago
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    |dw:1441062757048:dw|

  51. Trisaba
    • one year ago
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    thanks for the help

  52. dan815
    • one year ago
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    |dw:1441062793507:dw|

  53. dan815
    • one year ago
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    this is the full break down

  54. dan815
    • one year ago
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    they will probably ask u a final question like the chance it will rain, when there is a prediction of rain

  55. Trisaba
    • one year ago
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    60%

  56. Trisaba
    • one year ago
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    bayes' theorem

  57. Trisaba
    • one year ago
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    thanks for helping dan

  58. dan815
    • one year ago
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    wait i got 36% lemme see

  59. dan815
    • one year ago
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    okay think about it like this out of every 97 days, 5% of those days say it will rain, and it wont rain out of every 3 days, 90% of those days say it will rain, and it will rain! what is the total number of days it will rain to not raining then?

  60. Trisaba
    • one year ago
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  61. dan815
    • one year ago
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    0.03*0.9 : 0.05*0.97 this means that (0.03*0.9)/((0.03*0.9)+(0.05*0.97)) = chance it rains when it say it rains

  62. Trisaba
    • one year ago
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    60% is what i got

  63. dan815
    • one year ago
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    what did u say p(b) was

  64. Trisaba
    • one year ago
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    P(B) is .0755

  65. Trisaba
    • one year ago
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    look at my sheet posted pic

  66. dan815
    • one year ago
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    hard to read, what did u say P(B|A) was then

  67. Trisaba
    • one year ago
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    .9

  68. Trisaba
    • one year ago
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    \[\frac{ 90 }{ 151 }\]

  69. Trisaba
    • one year ago
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    it rounds to 60%

  70. dan815
    • one year ago
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    hmm i am not seeing anything wrong with the way im finding the answer, ill think about this more later but for now for every 100 days 3 days really rain 90% of 3 days is 2.7 so every 2.7 days out of the 3 days it rains, it will predict right now an additional bad predictions of 5% of 97 days is thrown in there 0.05*97=4.85 right preiction and rain = 2.7 total prediction of rainy days = 4.85+2.7 therefore 2.7/(4.85+2.7)= ~36%

  71. Trisaba
    • one year ago
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    |dw:1441064489549:dw|

  72. Trisaba
    • one year ago
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    what is the fill in

  73. dan815
    • one year ago
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    |dw:1441064723752:dw|

  74. dan815
    • one year ago
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    use that

  75. Trisaba
    • one year ago
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    ?

  76. dan815
    • one year ago
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    okay that is for 1 day

  77. dan815
    • one year ago
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    you do the same thing for 10,000 days

  78. dan815
    • one year ago
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    |dw:1441064976470:dw|

  79. dan815
    • one year ago
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    |dw:1441065024308:dw|

  80. Trisaba
    • one year ago
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  81. dan815
    • one year ago
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    fill it in

  82. dan815
    • one year ago
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    after u fill it in we can go over how to find it will rain given rain prediction if u still have to

  83. Trisaba
    • one year ago
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    got it done thanks

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