# Answer to Question #878 in Statistics and Probability for tasa

Question #878

Generally a new program may have the following types of errors: LOGIC error (L),

RUNTIME error (R) and SYNTAX error (S). The testing on the 80 new programs revealed;

18 programs had no errors; 5 programs had all three types errors; 14 programs had only

LOGIC errors; 6 programs had only RUNTIME errors; 17 programs had both SYNTAX and

RUNTIME errors; 12 programs had both SYNTAX and LOGIC errors.

a) Use a Venn diagram to illustrate the above problem including the given

numerical values. In your diagram, label with x and y the two region which

cannot be enumerated.

b) If the number of programs had SYNTAX error is the same as the number of

programs had LOGIC errors, derive a pair of simultaneous equations in terms

of x and y .

c) Solve the equations in b).

RUNTIME error (R) and SYNTAX error (S). The testing on the 80 new programs revealed;

18 programs had no errors; 5 programs had all three types errors; 14 programs had only

LOGIC errors; 6 programs had only RUNTIME errors; 17 programs had both SYNTAX and

RUNTIME errors; 12 programs had both SYNTAX and LOGIC errors.

a) Use a Venn diagram to illustrate the above problem including the given

numerical values. In your diagram, label with x and y the two region which

cannot be enumerated.

b) If the number of programs had SYNTAX error is the same as the number of

programs had LOGIC errors, derive a pair of simultaneous equations in terms

of x and y .

c) Solve the equations in b).

Expert's answer

<img src="/assignments/uploaded_files/operators_chat/123.png" alt="Venn diagram">

Logic = Syntax:

14 + 12 + X - 5 = Y + 12 + 17 - 5

14 + 6 + Y + 12 + 17 + X - 10 = 80

X - Y = 25

X + Y = 41

Y = 8

X= 33

Logic = Syntax:

14 + 12 + X - 5 = Y + 12 + 17 - 5

14 + 6 + Y + 12 + 17 + X - 10 = 80

X - Y = 25

X + Y = 41

Y = 8

X= 33

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