Question(s) about exercises in chapter 4

Hello! I have some problems with the exercises from chapter 4: I found a solution for ex. 4.1 (here it is), but it doesn't match exactly the actual solution, and I can't understand the solution proposed for ex. 4.2.

ex. 4.1 Given this statement:

suppose there is a probability y that an actual heads is reported as tails, or actual tails reported as heads.

I assumed the following:

P(data=T|coin=H) = y, which implies P(data=T|coin=H) = 1-y
P(data=H|coin=T) = y, which implies P(data=T|coin=T) = 1-y Given these probabilities I computed the new likelihood, but my result is swapped wrt/ the proposed solution, i.e. I get this (the full solution is in the above link):
```
if data=='H':
return (1-y)*x + y*(1-x)
else:
return y*x + (1-y)*(1-x)
```

Did I misinterpret the assignment? Or what?

ex. 4.2 Here I tried to follow the same reasoning to compute the likelihood, but I had to give up since I was not getting it. I looked at the proposed solution and I am not really understanding it.

Given the text in the solution:

Each article has a quality Q, which is the probability of eliciting an upvote from a completely reliable redditor. Each user has a reliability R, which is the probability of giving an upvote to an item with Q=1.

I would write it as follows in terms of probability: Q = P(vote=UP|R=1) R = P(vote=UP|Q=1)

Now of course the likelihood is (as stated in the solution):

The probability that a redditor with reliability R gives an upvote to an item with quality Q

but I can't understand the solution itself, i.e. I can't obtain it when writing it down in terms of probability:

P(vote=UP|R,Q) = ... ?

What am I missing? Can anyone please help?

PS: since I already wrote a lot, adding these few words won't hurt: I love this book, great work Allen!

AllenDowney / ThinkBayes2

Question(s) about exercises in chapter 4 #21