We continue with the setup described in Exercise $4\mathrm{.}27.$

$($a$)$ Suppose that $\backslash$delta $=9$

$10$

and p $=3$

$4$

$.$ If we run the algorithm $25$ times on the

input m andalwaysgetbackNo, what is the probability that m does not have

property A$?$

$($b$)$ Same question as $($a$),$ but this time we run the algorithm $100$ times.

$($c$)$ Suppose that $\backslash$delta $=99$

$100$

and p $=1$

$2$

$.$ How many times should we run the algorithm

on m to be $99\%$ confident that m does not have property A$,$ assuming that

every output is No$?$

$($d$)$ Same question as $($c$),$ except now we want to be $99\mathrm{.}9999\%$ confident