Answer:
The probability that a person is guilty given that he or she denies the knowledge of the error is 0.6068.
Step-by-step explanation:
The Bayes' theorem states that the conditional probability of an event <em>E</em>, belonging to the sample space S, given that another event <em>A</em> has already occurred is:
Denote the events as follows:
<em>X</em> = illegal deduction is filed
<em>Y</em> = knowledge of the error is denied.
The information given is:
P (Cheating) = 0.06
P (Actual error) = 0.03
P (Y|X) = 0.76
Compute the probability of <em>X</em> as follows:
The probability that a person who is not guilty will deny the knowledge of the error, is:
Compute the value of P (X|Y) as follows:
Thus, the probability that a person is guilty given that he or she denies the knowledge of the error is 0.6068.