chapter 07 of the book "Introduction to Probability, 2nd Edition" gives this example
above is the first part, where everything is cool.
to understand this, I would like to identify the day with Monday, Tuesday, Wednesday, Thursday and Friday.
The machine is working on Monday.
the probability that The machine will be working Tuesday is $1-b$, whereas the probability that The machine will break down Tuesday is b.
is the probability that The machine will break down again (twice in total) Wednesday $1-r$ or $b(1-r)$? I'll choose the last, and I need a double check.