Average entropy. Let H$($p$)=-$ p $*$ log$\_2($p$)-(1-$ p$)*$ log$\_2(1-$ p$)$ be the binary entropy function.

$($a$)$ Evaluate H$(1/4)$ using the fact that log$\_2(3)\backslash$approx $1\mathrm{.}584($Hint: You may wish to consider an experiment with four equally likely outcomes, one of which is more interesting than the others.$)$