swerve326 swerve326
  • 23-01-2020
  • Computers and Technology
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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?

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Debel
Debel Debel
  • 23-01-2020

Answer:

2048

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 [tex]n^{N}[/tex] = [tex]2^{11}[/tex] = 2048

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

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