Question

Errors in the programming language Python can be broadly classified into two types, syntax errors, and logical errors. When writing a program the first time, the probability for syntax errors to arise is 0.3, that for logical errors is 0.5, and that for both errors to occur is 0.1.(a) Find the probability that no syntax errors occur.(b) Find the probability that no errors occur.(c) Find the probability that errors of any type occur.(d) The programmer found a syntax error in the code. What is the probability that there are also logical errors based on this finding?(e) Are the events of having syntax errors and logical errors independent? Also, explain why.

Answer 1

Explanation:

a( Pr(no syntax error) = 1-Pr(syntax error arises)

Pr(no syntax error) = 1 -0.3

Pr(no syntax error) = 0.7

b) Pr(no error occurred) = 1-Pr(both error occurred)

Pr(no error occurred) = 1-0.1

Pr(no error occurred) = 0.9

c) Pr(any type of error occurred) = Pr(syntax error occur)+Pr(logical)

Pr(any type of error occurred) = 0.5+0.3 = 0.8

d) Pr(syntax and logical) = Pr(syntax occur)+Pr(logical or syntax occur)

= 0.3+0.1

= 0.4

e) Independent event are events that occurs at the same time. The occurrence of one does not affect the other.

Pr(logical and syntax) = pr(syntax)×pr(logical)

Given

pr(syntax)×pr(logical) = 0.3×0.5 = 0.15

From the question, Pr(logical and syntax) = Pr(both error occurred) = 0.1

Since Pr(logical and syntax) ≠ pr(syntax)×pr(logical), this means that the errors are not independent