Exponential rv problem

[omri assaf]

A man arrives to the bus station.
If the bus arrive to the station within 10 minutes the man returne home by bus
Else - he walk back home and it takes him 10 minutes
Bus arrival time is exponentially distributed with parameter = 1/8 minutes
Bus riding time is exponentially distributed with parameter = 1/12

A. What is the probability that the man will arrive home in 20 minutes maximum (t<=20)

B.what is the mean of the time length the man waits every day

 

[Steven G]

Nice problem. Can you please tell us where you are stuck so that we can help you?

 

[omri assaf]

A. P = (no problem here) p1(case in which we wait 10 minutes and walk 10 minutes) + (here I have the problem) p2(station waiting + walk time). I know p2 supposed to be calculated by conditional probability but I'm not sure how to solve it. Thank you!