Question

A wireless garage door opener has a code determined by the up or down setting of 11 switches. How many outcomes are in the sample space of possible codes?

Answer 1

2048

Step-by-step explanation:

we are given the total number of switches (N) to be = 11

The number of possible outcome for each switch (n) is = 2 ( up and down)

Therefore all possible outcomes in the sample space of possible codes will be
`n^(N)` =
`2^(11)` = 2048

The sample space can be represented like this :
`s=\{ (x_(1),x_(2),x_(3),...,x_(11))|x_(1),x_(2),x_(3),...,x_(11)\in\{up,down\} \}`