## Tricky problem about 9 houses

Ace Home Inspectors inspect nine houses each business day.
Because AHI has been keeping records for several years they know
that the probability of all nine houses passing inspection in a
single day is 70%, the probability of eight houses passing on a
single day is 20%, of seven houses passing on a single day 9%.
Assume that the inspection results are totally independent of
one another.

Now suppose that nine houses are inspected (on a single day). Two
of the nine inspection reports are selected at random, and both of
those houses passed inspection.
a) What is the probability that the remaining seven also passed?
b)Suppose that a business week for AHI is 5 days long. What is the
probability that there will be exactly one failed inspection that week?

a)Actually I think it is given to us because each single day the probability for 7 houses is 9%. So remaining 7 houses have 9% of probability. Or I think totally wrong...

b) I think here I just need to use complement rule....which means p(failed) = 1- 0.7 = 0.3...

I know that two answers are pretty wrong...But I have no any idea how to solve it..... Help me please with this problem..thanks..