$5.$ A market analyst determines $61\mathrm{.}3\%$ of mid$-$cap funds available to be added to his client$$s portfolio outperformed their

S&P benchmarks over the past $3$ years.

$($a$)$ When choosing funds at random, what is the likelihood the first fund to outperform its benchmark happens in less

than six tries?

$($b$)$ What is the likelihood in a random group if $12$ funds, at least eight outperform their benchmarks?