$8\mathrm{.}5.$ The average annual rainfall over a certain area is estimated to be $1524mm,$ and the rainfall is as likely to be above average in any year $($wet year$)$ as it is to be below average $($dry year$).$ For any $20-$year interval, what is the probability of experiencing the following events: $($a$)$ one wet year with $19$ dry years, and $($b$)10$ wet years with $10$ dry years?