Question

I AWARD METALS!!
Urgent! Need help ASAP please!

Choose a row and column and compare P(A | B) with P(B | A). Explain what each probability means in the context of the situation and data you collected.

Answer 1

My chart is:
Krispy Kreme Dunkin Doughnuts
Home 5 2
Bakery 7 6

Answer 2

The theme for the chart is "Do you prefer Krispy Kreme or Dunkin' Doughnuts and do you prefer to eat it at home or at the bakery?

Answer 3

Thank you @TassMagger for tagging people!!!

Answer 4

\(\large

\begin{array}{|c|c|}
\hline
\text{Type}&\text{Krispy Kreme}&\text{Dunkin Doughnuts}\\
\hline
\text{Home}&\color{red}{5}&\color{red}{2}\\
\hline
\text{Bakery}&\color{red}{7} &\color{red}{6}\\
\hline

\end{array}
\)

Answer 5

Choose a row and column and compare P(A | B) with P(B | A)

Answer 6

lets say,

\(A\) represents \(Home\)
\(B\) represents \(Krispy~Kreme\)

Answer 7

then, \(P(A | B)\) means the probability for \(Home\), given that it is \(Krispy ~ Kreme\)

Answer 8

Look at the \(Krispy ~Kreme\) column

Answer 9

how many are \(Home\) ?

Answer 10

5

Answer 11

So would it be 5/12? Since 5+7=12

Answer 12

yes, and the total in that column is 5+7 = 12
so probability for \(Home\), given that its \(Krispy~ Kreme\) is :

\(\large P(A | B) = \frac{5}{12}\)

Answer 13

you got it !!

Answer 14

lets find out \(\large P(B|A)\)

Answer 15

Look at \(Home\) row

Answer 16

OOOH I get it now! Thank you so much! Okay :) So it would be 7/12?

Answer 17

I meant 2/12 sorry

Answer 18

nope

Answer 19

\(
\large

\begin{array}{|c|c|}
\hline
\text{Type}&\text{Krispy Kreme}&\text{Dunkin Doughnuts}\\
\hline
\text{Home}&\color{red}{5}&\color{red}{2}\\
\hline
\text{Bakery}&\color{red}{7} &\color{red}{6}\\
\hline

\end{array}
\)

Answer 20

or no. Sorry 2/8=1/4

Answer 21

Look at \(Home\) ROW

Answer 22

how many are \(Krispy~Kreme\) ?

Answer 23

5

Answer 24

yes, and in \(Home\) row, we have a total of 5+2 = 7

So, probability for \(Krispy ~Kreme\) , given that its \(Home\) is :
\(\large P(B|A ) = \frac{5}{7}\)

Answer 25

Okay so when we figured out P(A|B) we looked at the krispy kreme column and got 5/12. Now for P(B|A), we look at the Home row and get 5/7 because 5+2=7. I get how we got the probability, but why do we compare the row for P(B|A) and the column for P(A|B)?

Answer 26

very good question :)

let me ask u a question first :-

what are \(A\) and \(B\) here ?

Answer 27

Thank you ☺ A would be Home. B is Krispy Kreme.

Answer 28

A represents Home
B represents Krispy Kreme

Answer 29

yes :)

Answer 30

and one more q :-

wat does \(P(A | B) \)represent ?

Answer 31

say it in words..

Answer 32

Would it be the probability of Home in the Krispy Kreme column?

Answer 33

Nope.

Answer 34

\(P(A | B)\) should be read literally as below :

"Probability of \(A\), \(given\) that \(B\) already happened"

Answer 35

the vertical bar "|" should be read as "given"

Answer 36

Oh okay

Answer 37

Since \(B\) represents \(Krispy~ Kreme\),

\(P(A | B)\) should be read as : Probabolity of \(A\), given that "\(Krispy~Kreme\)" already happened

Answer 38

so, we're bothered only about the "Krispy Kreme" Column,
cuz we have the information that its already "Krispy Kreme"

Answer 39

OH okay that makes more sense!

Answer 40

do 1-2 more problems,
and everything will make sense.... these look hard in the start, but very easy once u get hang of how to do..

Answer 41

So would that be why we do the home row with P(B|A)? We are only bothered by the home row because we have the information that is already home?

Answer 42

Exactly ! you got it !!!

Answer 43

YAY! Okay!! Thank you SOO much! It is much clearer to me now!! I have 3 more questions but I will try to do them on my own first, and if I have any questions about them, can I ask you?

Answer 44

sure... just holler when u feel stuck on anything... good luck !

Answer 45

Okay ☺ I will! Thank you very much!

Answer 46

np... u wlc :)b

Answer 47

Okay so my answer to that question is:
A represents Home
B represents Krispy Kreme
P(A|B) means that we will be getting the probability of the chance that people like to eat at home when they get Krispy Kreme. So we will be looking at home in the Krispy Kreme column. The reason we are looking at the Krispy Kreme column is because (A|B) means the probability of A given that B has already happened. The | means given. In simpler terms for the question, we are bothered by the Krispy Kreme column because we have all of the information for Krispy Kreme.

In the Krispy Kreme column, 5 are home.
In the home column total, we have 12 since 5+7=12.
So the probability of P(A|B) is 5/12.

Now, let’s look at P(B|A).
We are comparing the home row now. We are finding the probability of eating Krispy Kreme at home versus eating Dunkin Donuts at home. We are bothered by the home row because we have all of the information of the Home row and we are only finding the probability of Krispy Kreme at home versus Dunkin Donuts at home instead of the other way around because A represents home, and B represents Krispy Kreme.
In the Krispy Kreme column, 5 are home.
In the home row total, we have 7 since 5+2=7.
So the probability that people eat Krispy Kreme at home versus people eating Dunkin Donuts at home is 5/7.

Does that sound right?

Answer 48

Okay so my answer to that question is:
A represents Home
B represents Krispy Kreme
P(A|B) means that we will be getting the probability of the chance that people like to eat at home when they get Krispy Kreme. So we will be looking at home in the Krispy Kreme column. The reason we are looking at the Krispy Kreme column is because (A|B) means the probability of A given that B has already happened. The | means given. In simpler terms for the question, we are bothered by the Krispy Kreme column because we "have the information that Kirspy Kreme occurred already, so other columns are useless"(have all of the information for Krispy Kreme.)

In the Krispy Kreme column, 5 are home.
In the home column total, we have 12 since 5+7=12.
So the probability of P(A|B) is 5/12.

Now, let’s look at P(B|A).
We are comparing the home row now. We are finding the probability of eating Krispy Kreme at home versus eating Dunkin Donuts at home. We are bothered by the home row because we "have the information that Home occurred already, so other rows are useless"(have all of the information of the Home row) and we are only finding the probability of Krispy Kreme at home versus Dunkin Donuts at home instead of the other way around because A represents home, and B represents Krispy Kreme.
In the Krispy Kreme column, 5 are home.
In the home row total, we have 7 since 5+2=7.
So the probability that people eat Krispy Kreme given that it is Home is 5/7.

Answer 49

^changed only slightly
overall it is looking vey good !! good work :)