Answer:
Kindly check explanation
Step-by-step explanation:
Acceptable = a
Fails = f
For machines X, Y, Z ;
Sample space, S = {aaa, aaf, aff, fff, faa, afa, ffa, faf}
Total elements in sample space = 8
B.)
Elements of the set:
ZF={circuit from Z fails},
XA ={circuit from X is acceptable}.
ZF = {aaf, aff, fff, faf}
XA = {aaa, aaf, aff, afa}
C.)
c. Are ZF and XA mutually exclusive?
Check if ZF n XA = ∅
ZF n XA = {aaf, aff}
Hence, ZF and XA are not mutually exclusive
d. Are ZF and XA collectively exhaustive?
To be collectively exhaustive :
ZF u XA = Sample space
ZF u XA = {aaa, aaf, aff, afa, faf, fff}
{aaa, aaf, aff, afa, faf, fff} ≠ sample space
Hence, ZF and ZA are not collectively exhaustive.
e. What are the elements of the sets
C={more than one circuit acceptable},
C = {aaa, aaf, faa, afa}
D={at least two circuits fail}.
D = {ffa, faf, aff, fff}
f. Are C and D mutually exclusive?
Check if C n D = ∅
C n D = ∅
Hence, A and D are mutually exclusive
g. Are C and D collectively exhaustive?
To be collectively exhaustive :
C u D = Sample space
C u D = {aaa, aaf, aff, afa, faf, fff}
{aaa, aaf, faa, ffa, aff, afa, faf, fff} = sample space
Hence, C and D are collectively exhaustive.
