Checking my results for Bayesian updating

Question

I'd really appreciate if someone could tell me whether I've completed the following questions regarding Bayesian updating correctly. I've been struggling with this topic for a while but I think I'm getting the hang of it. There aren't any answers available to me for these questions though so I'm not totally sure if I'm correct:

Question 1

My answer:

Three possible cases (001, 010, 100). Two outcomes per query (0, 1).

After final query;
x     || 001 | 010 | 100
P(x)  || 4/21|16/21| 1/21

Question 2

My answer:

Four cases (a, b, 4, 8). Four outcomes (a, b, 4, 8).

After final query;
x     ||  a  |  b  |  4  |  8
P(x)  || 1/6 | 1/6 | 1/3 | 1/3    

Question 3

My answer:

Two cases (W1, W2). Three outcomes (1, 2, 3)

After final query;
x     ||  W1 |  W2
P(x)  || 3/15| 12/15  

...

So, do those answers seem correct? I appreciate this is a lot of work to ask for but it would really help. Thanks in advance!

Answer 1

I found a YouTube video which works through question 1. My answer is correct. I hope that means I got the other two right as well, but I would still like confirmation.

The video in question:

https://www.youtube.com/watch?v=tKpmHnbqGTs