A Probability Problem of Using a Washing Machine

Last night when coming back to the dorm,
I kept thinking probability problems.

I put clothes into the washing machine,
meanwhile, I was thinking:
There're 8 rooms each row, so there're 8*4=32 people totally.
Given that every one has identical frequency of washing clothes.
and given that no one wash their clothes in midnight and on the early morning,
all people wash clothes only in 24-16=8 hours.

Therefore, there're 32/7/16=0.29 people per hour averagely.
So about 0.21 people per 45 minutes.
Next we assumt that the washing events between people are mutually indepent,
It's a Poisson Distribution.

So when you go washing your clothes,
the probability of seeing an empty washing machine
(i.e., you can use it right away)
equals to the probability that no one use the machine
in the last 45 minutes,
which is about p(0)=exp(-0.21)=0.81

Conclusively, you will see an empty washing machine
around 4 times per 5 times averagely.