please answer $5$ and show workProblem $5$:

Your bottleneck machine is found to breakdown from two main causes, misfeeds $(30\%)$ or overheating

$(70\%).$ Given a misfeed, the two possible root causes are: operator error $(32\%)$ or defective materials

$(68\%).$ Given that overheating occurs, the three possible root causes are: fan issues $(26\%),$

environmental factors $(17\%),$ or improper settings $(57\%).$

$($a$)$ Calculate the probability that the breakdown of the bottleneck machine is caused by a operator

error.

$($b$)$ Calculate the probability that the breakdown of the bottleneck machine is caused by a fan issue

or improper settings.