A certain part of a machine can be in one of two states: working (W) or undergoing
repair (R). A working part fails during the course of a day with probability a; assume
that failure occurs at the end of the day so that the part can be labelled as in working
condition for that day. Having failed, it undergoes repair on the following working day.
The probability that a part undergoing repair is in working order by the start of the
following working day is b.
Assume that the part is in working condition on Monday morning. What is the probability
that it is working on Wednesday (2 days later)?
I have gotten (1-a)^2+(1-a)ab but i am not sure if i have done it wrong. I have basically used a tree diagram and used the appropriate branches.Can anyone check my solution because there is no answer for the odd questions in the book
W'=it has wrecked at the end of the day:
Therefore i get:
1) it is working at the end of monday and it is working at the end of tuesday and therefore ready at the start of
2)it is working at the end of monday, but fails at the end of tuesday but is repaired on wednesday in time for use on wednesday
I am not 100% certain can someone else try this?
It should be 2) it fails on monday (but we consider it working on monday because it started out working), but is repaired on tuesday, giving ab.