A circuit designer is developing a new digital system that utilizes a $4-$bit binary code to encode various input values.

Each bit in the code can assume a value of either $0$ or $1.$

Let's assume the designer randomly selects one of the potential $4-$bit binary codes as the input and records the sum of the bits as the outcome.

For this random experiment, define the correspoding Sample Space $S,$ the Set of Possible Events $,$ and the corresponding Probabilities $P.($please explain in depth$)$ especialliy sample space, for sample space i have been given this hint ncorrect Sample Space. Outcome of the experiment is the sum of the bits, i$.$e$.0,1,2,3,4$;

Set of the events would be:

$\{$empty$\},\{0\},\{1\},\{0,1\},\{2\},\{2,0\},\{2,1\},\{2,1,0\}...$ and so on$.$ There should be $32$ events.

Probabilities should be only assigned to elementary events: $\{0\},\{1\},\{2\},\{3\},\{4\}.$

it is $2^5$ and not $2^4$