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...

- Trisaba

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- Trisaba

made a good decision? why or why not?

- Trisaba

this is a series of questions

- Trisaba

@dan815

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## More answers

- Trisaba

what is probability of b given a

- Trisaba

P(B l A)

- dan815

okay what is B and A

- Trisaba

in the question

- Trisaba

last two lines

- dan815

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

- Trisaba

b given a

- dan815

okay so chance the forecast predicts right given it rains then

- dan815

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

- dan815

P(B|A)=0.9=90%

- 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

no not times P(A) formula above

- Trisaba

how did you figure out that the second thing was that

- dan815

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

- Trisaba

yeah

- dan815

because the statement is already telling us what we want

- Trisaba

no

- Trisaba

P(A) at bottom

- Trisaba

how did you know it was it

- dan815

oh sry ya p(a) bottom

- dan815

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

- dan815

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

- Trisaba

oh

- Trisaba

now what is P(A)

- Trisaba

now what is P(A)

- dan815

3% chance it rains on a day in june

- Trisaba

is a?

- dan815

ya

- Trisaba

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

- Trisaba

.97?

- dan815

|dw:1441061445919:dw|

- dan815

or100%-3%= 1-0.03

- dan815

yes compliment raining is not raining, which is 97%

- Trisaba

P(B l A complement) is?

- dan815

that means chance of prediction when there is no rain

- dan815

|dw:1441061765626:dw|

- Trisaba

5%?

- dan815

yeah

- Trisaba

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

- Trisaba

|dw:1441062094509:dw|

- Trisaba

a complement we said was .97

- dan815

yeah

- Trisaba

so what are the question marks

- dan815

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

- dan815

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

- dan815

|dw:1441062757048:dw|

- Trisaba

thanks for the help

- dan815

|dw:1441062793507:dw|

- dan815

this is the full break down

- dan815

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

- Trisaba

60%

- Trisaba

bayes' theorem

- Trisaba

thanks for helping dan

- dan815

wait i got 36% lemme see

- 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

##### 1 Attachment

- 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

60% is what i got

- dan815

what did u say p(b) was

- Trisaba

P(B) is .0755

- Trisaba

look at my sheet posted pic

- dan815

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

- Trisaba

.9

- Trisaba

\[\frac{ 90 }{ 151 }\]

- Trisaba

it rounds to 60%

- 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

|dw:1441064489549:dw|

- Trisaba

what is the fill in

- dan815

|dw:1441064723752:dw|

- dan815

use that

- Trisaba

?

- dan815

okay that is for 1 day

- dan815

you do the same thing for 10,000 days

- dan815

|dw:1441064976470:dw|

- dan815

|dw:1441065024308:dw|

- Trisaba

##### 1 Attachment

- dan815

fill it in

- 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

got it done thanks

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