## 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...

1. Trisaba

made a good decision? why or why not?

2. Trisaba

this is a series of questions

3. Trisaba

@dan815

4. Trisaba

what is probability of b given a

5. Trisaba

P(B l A)

6. dan815

okay what is B and A

7. Trisaba

in the question

8. Trisaba

last two lines

9. dan815

P(B|A) means A given B or B given A?

10. Trisaba

b given a

11. dan815

okay so chance the forecast predicts right given it rains then

12. dan815

when it rains, the forecast correctly predicts rain 90% of the time.

13. dan815

P(B|A)=0.9=90%

14. Trisaba

a formula for P(B l A) is that is P(A intersection B) times P(A) all divided by P(B)

15. Trisaba

?

16. Trisaba

no not times P(A) formula above

17. Trisaba

how did you figure out that the second thing was that

18. dan815

P(B|A)=P(a n b)/P(b) like that?

19. Trisaba

yeah

20. dan815

because the statement is already telling us what we want

21. Trisaba

no

22. Trisaba

P(A) at bottom

23. Trisaba

how did you know it was it

24. dan815

oh sry ya p(a) bottom

25. dan815

P(B|A) is asking the probability of B given A probability of rain prediction when it rains

26. dan815

and this statement is giving you the answer "when it rains, the forecast correctly predicts rain 90% of the time. "

27. Trisaba

oh

28. Trisaba

now what is P(A)

29. Trisaba

now what is P(A)

30. dan815

3% chance it rains on a day in june

31. Trisaba

is a?

32. dan815

ya

33. Trisaba

$P \left( a ^{c} \right)$ is what

34. Trisaba

.97?

35. dan815

|dw:1441061445919:dw|

36. dan815

or100%-3%= 1-0.03

37. dan815

yes compliment raining is not raining, which is 97%

38. Trisaba

P(B l A complement) is?

39. dan815

that means chance of prediction when there is no rain

40. dan815

|dw:1441061765626:dw|

41. Trisaba

5%?

42. dan815

yeah

43. Trisaba

$P(A) \times P(B l A) + P(A ^{c}) \times P(B l A ^{c})=P(B)$

44. Trisaba

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45. Trisaba

a complement we said was .97

46. dan815

yeah

47. Trisaba

so what are the question marks

48. dan815

when it does not rain, the forecast predits 95% of the time it wont rain and 5% it will rain

49. dan815

that what it means by 5% wrong prediction when it does not rain

50. dan815

|dw:1441062757048:dw|

51. Trisaba

thanks for the help

52. dan815

|dw:1441062793507:dw|

53. dan815

this is the full break down

54. dan815

they will probably ask u a final question like the chance it will rain, when there is a prediction of rain

55. Trisaba

60%

56. Trisaba

bayes' theorem

57. Trisaba

thanks for helping dan

58. dan815

wait i got 36% lemme see

59. dan815

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

61. dan815

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

60% is what i got

63. dan815

what did u say p(b) was

64. Trisaba

P(B) is .0755

65. Trisaba

look at my sheet posted pic

66. dan815

hard to read, what did u say P(B|A) was then

67. Trisaba

.9

68. Trisaba

$\frac{ 90 }{ 151 }$

69. Trisaba

it rounds to 60%

70. dan815

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

|dw:1441064489549:dw|

72. Trisaba

what is the fill in

73. dan815

|dw:1441064723752:dw|

74. dan815

use that

75. Trisaba

?

76. dan815

okay that is for 1 day

77. dan815

you do the same thing for 10,000 days

78. dan815

|dw:1441064976470:dw|

79. dan815

|dw:1441065024308:dw|

80. Trisaba

81. dan815

fill it in

82. dan815

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

got it done thanks