Please Investigate Question #4 on this Exam

Hey Team,

Thanks for your hard work on this class. I really appreciate it. I've been working to understand how the instructor arrived at this answer, and I just don't get it. I've done the calculations by hand, and they don't add up to what he shows in the answer.

I get these values for S1, S2, and S3 respectively:

0.036, 0.286, 0.071

Can you please double check his steps here and ensure he did this properly and explain it to me if so.

Here is an error, as far as I can see. He says that S2 must be 4 TIMES more likely than S1.

But let's look at the total probability of S2: 0.2 * 2 = 0.4.
Now, total probability of S1: 0.05 * 4 = 0.2.

Is 0.4 actually 4 times 0.2?

0.4/ 0.2 = 2. So it's only twice more likely, not 4 times more likely. If I have messed up this logic, what did I do wrong? Thanks!