Trisaba
  • Trisaba
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...
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
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Trisaba
  • Trisaba
made a good decision? why or why not?
Trisaba
  • Trisaba
this is a series of questions
Trisaba
  • Trisaba
@dan815

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Trisaba
  • Trisaba
what is probability of b given a
Trisaba
  • Trisaba
P(B l A)
dan815
  • dan815
okay what is B and A
Trisaba
  • Trisaba
in the question
Trisaba
  • Trisaba
last two lines
dan815
  • dan815
P(B|A) means A given B or B given A?
Trisaba
  • Trisaba
b given a
dan815
  • dan815
okay so chance the forecast predicts right given it rains then
dan815
  • dan815
when it rains, the forecast correctly predicts rain 90% of the time.
dan815
  • dan815
P(B|A)=0.9=90%
Trisaba
  • Trisaba
a formula for P(B l A) is that is P(A intersection B) times P(A) all divided by P(B)
Trisaba
  • Trisaba
?
Trisaba
  • Trisaba
no not times P(A) formula above
Trisaba
  • Trisaba
how did you figure out that the second thing was that
dan815
  • dan815
P(B|A)=P(a n b)/P(b) like that?
Trisaba
  • Trisaba
yeah
dan815
  • dan815
because the statement is already telling us what we want
Trisaba
  • Trisaba
no
Trisaba
  • Trisaba
P(A) at bottom
Trisaba
  • Trisaba
how did you know it was it
dan815
  • dan815
oh sry ya p(a) bottom
dan815
  • dan815
P(B|A) is asking the probability of B given A probability of rain prediction when it rains
dan815
  • dan815
and this statement is giving you the answer "when it rains, the forecast correctly predicts rain 90% of the time. "
Trisaba
  • Trisaba
oh
Trisaba
  • Trisaba
now what is P(A)
Trisaba
  • Trisaba
now what is P(A)
dan815
  • dan815
3% chance it rains on a day in june
Trisaba
  • Trisaba
is a?
dan815
  • dan815
ya
Trisaba
  • Trisaba
\[P \left( a ^{c} \right)\] is what
Trisaba
  • Trisaba
.97?
dan815
  • dan815
|dw:1441061445919:dw|
dan815
  • dan815
or100%-3%= 1-0.03
dan815
  • dan815
yes compliment raining is not raining, which is 97%
Trisaba
  • Trisaba
P(B l A complement) is?
dan815
  • dan815
that means chance of prediction when there is no rain
dan815
  • dan815
|dw:1441061765626:dw|
Trisaba
  • Trisaba
5%?
dan815
  • dan815
yeah
Trisaba
  • Trisaba
\[P(A) \times P(B l A) + P(A ^{c}) \times P(B l A ^{c})=P(B)\]
Trisaba
  • Trisaba
|dw:1441062094509:dw|
Trisaba
  • Trisaba
a complement we said was .97
dan815
  • dan815
yeah
Trisaba
  • Trisaba
so what are the question marks
dan815
  • dan815
when it does not rain, the forecast predits 95% of the time it wont rain and 5% it will rain
dan815
  • dan815
that what it means by 5% wrong prediction when it does not rain
dan815
  • dan815
|dw:1441062757048:dw|
Trisaba
  • Trisaba
thanks for the help
dan815
  • dan815
|dw:1441062793507:dw|
dan815
  • dan815
this is the full break down
dan815
  • dan815
they will probably ask u a final question like the chance it will rain, when there is a prediction of rain
Trisaba
  • Trisaba
60%
Trisaba
  • Trisaba
bayes' theorem
Trisaba
  • Trisaba
thanks for helping dan
dan815
  • dan815
wait i got 36% lemme see
dan815
  • 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?
Trisaba
  • Trisaba
dan815
  • 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
Trisaba
  • Trisaba
60% is what i got
dan815
  • dan815
what did u say p(b) was
Trisaba
  • Trisaba
P(B) is .0755
Trisaba
  • Trisaba
look at my sheet posted pic
dan815
  • dan815
hard to read, what did u say P(B|A) was then
Trisaba
  • Trisaba
.9
Trisaba
  • Trisaba
\[\frac{ 90 }{ 151 }\]
Trisaba
  • Trisaba
it rounds to 60%
dan815
  • 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%
Trisaba
  • Trisaba
|dw:1441064489549:dw|
Trisaba
  • Trisaba
what is the fill in
dan815
  • dan815
|dw:1441064723752:dw|
dan815
  • dan815
use that
Trisaba
  • Trisaba
?
dan815
  • dan815
okay that is for 1 day
dan815
  • dan815
you do the same thing for 10,000 days
dan815
  • dan815
|dw:1441064976470:dw|
dan815
  • dan815
|dw:1441065024308:dw|
Trisaba
  • Trisaba
dan815
  • dan815
fill it in
dan815
  • dan815
after u fill it in we can go over how to find it will rain given rain prediction if u still have to
Trisaba
  • Trisaba
got it done thanks

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