Problem $5($Probability of a Code Word$)$: $(10$ points$)$ Consider a binary code with $5$ bits $(0$

or $1)$ in each code word. An example of a code word is $01010.$ In each code word, a bit is a zero

with probability $0\mathrm{.}8,$ independent of any other bit.

$($a$)$ What is the probability of the code word $00111?$

$($b$)$ What is the probability that a code word contains exactly three ones?