[tex]A \ system \ is \ composed \ o f \ 5 \ components \ , \ e ach \ of \ which \ is \ either \ working \ or[/tex][tex]failed. \ Consider \ an \ experiment \ that \ consists \ of \ observing \ the \ status \ of \ each[/tex][tex]component \ . and \ let \ the \ outcome \ of \ the \ experiment \ be \ given \ by \ the \ vector[/tex][tex](x1,x2,x3, x4, x5), \ where \ xi \ is \ equal \ to \ 1\ if \ component \ i \ is \ working \ and \ is \\ equal \ to \ 0 \ if \ component \ i \ is \ failed.[/tex]
[tex](a) \ How \ many \ outcomes \ are \ in \ the \ sample \ space \ of \ this \ experiment?[/tex]
[tex](b) \ Suppose \ that \ the \ system \ wil l \ work \ if \ components \ 1 \ and \ 2 \ are \ both \\ working, or \ if \ components \ 3 \ and \ 4 \ are \ both \ working, \ or \ if \ components \ 1, \ 3, \\ and \ 5 \ are \ all \ working. \ Let \ W \ be \ the \ event \ that \ the \ system \ will \ work. \ Specify \\ all \ the \ outcomes \ i n \ W.[/tex]
Answer:
Step-by-step explanation:
From the given information:
We learned that it is possible that all entities can be in one of two states i.e. 0 or 1. Thus, all 5 entities can either be 0 or 1 (2 states).
∴
Number of outcomes = 2 × 2 × 2 × 2 × 2
= 2⁵
= 32
b)
All the outcomes of W = {(1, 1, x₃, x₄, x₅) (x₁, x₂, 1, 1, x₅) (1, x₂, 1, x₄, 1)}
