Why are we subtracting 1 from each bowl (Chapter 2 Exercise: cookie problem)

[allendowney]

Why are we subtracting 1 from each bowl (Chapter 2 Exercise: cookie problem)

[AllenDowney]

Yes, I see why this is confusing, but I think the solution is correct. The first Hist represents the hypothesis that we are drawing from Bowl 1. The second represents the hypothesis that we are drawing from Bowl 2. When we draw the first cookie, we compute the likelihood of the data based on the old proportions. And then we update the proportions. When we draw the second cookie, we want to compute P(data | both cookies are from Bowl 1) and P(data | both cookies are from Bowl 2) So in both cases we should use the update proportions. You are right that in the first scenario, Bowl 2 is unchanged. And in the second scenario, Bowl 1 is unchanged. But since we never refer to the proportions in the unused bowl, I didn't bother to represent it. What do you think? Allen

…

On Sun, Jul 12, 2020, at 9:10 AM, A.Srivastava wrote: IMG_20200712_150712 <https://user-images.githubusercontent.com/41738944/87247064-ac47c080-c451-11ea-886e-7059fcf03f77.jpg> — You are receiving this because you commented. Reply to this email directly, view it on GitHub <#28 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAOLP3KFNDHTLD732RBLJULR3GY2VANCNFSM4OXLQ4WQ>.

[AllenDowney]

Which file are you looking at?

[akshat1995-sc]

I am looking at 'cookie_soln.ipynb' in solutions folder.

[akshat1995-sc]

[akshat1995-sc]

What I mean to state is that, there would be four different outcomes in the 2nd draw.
P(B1 | Choc, A_1), P(B2 | Choc, A_1), P(B1 | Choc, B_2), P(B2 | Choc, B_2).
with the notations as follows:
A: Vanilla draw from bowl 1
B: Vanilla draw from bowl 2
A_1 : Event A in draw no.1
A_2 : Event A in draw no. 2
B1: current draw from bowl 1
B2: current draw from bowl 2

Is it clearer?

[akshat1995-sc]

I attempted to evaluate the following values using the aforementioned table (i.e the updated content of bowls) in picture above.
P(data | both cookies are from Bowl 1), and
P(data | both cookies are from Bowl 2)

The result is quite different from the ones obtained in 'cookie_soln.ipynb'. Please check the image. Do you think I am missing something?

[akshat1995-sc]

Was the above solution confusing? I simply attempted to extend the suggested probabilities on paper.