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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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
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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.

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

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