A company is considering using a polygraph to screen the “honesty” of their applicants. When asked, “Have you ever stole anything from your place of work?”… everyone naturally answers “No”, however, based on past experience, the company believes that 8% of their applicants are being dishonest when answering this question. In a polygraph test, a “positive result” means a response statement is identified as a lie. While widely used, polygraphs are not very accurate. Research has shown that a polygraph can correctly detect 65% of lies told, but incorrectly identifies 15% of true statements as lies. Based on the given probabilities, answer the following questions: Are the events that an applicant is dishonest and identified as a liar independent? Are these events mutually exclusive? Can mutually exclusive events be independent events? Consider the following steps in order to respond to the questions above Step 1: Identify and define the two events and their complements. Correctly label the probabilities given using the defined events and their complements Step 2. Make a Tree diagram. Compute the probability that an applicant is identified as a liar. Calculate the probability that an applicant is dishonest given that they are identified as a liar.
A company is considering using a polygraph to screen the “honesty” of their applicants. When asked, “Have you ever stole anything from your place of work?”… everyone naturally answers “No”, however, based on past experience, the company believes that 8% of their applicants are being dishonest when answering this question. In a polygraph test, a “positive result” means a response statement is identified as a lie. While widely used, polygraphs are not very accurate. Research has shown that a polygraph can correctly detect 65% of lies told, but incorrectly identifies 15% of true statements as lies.
Based on the given probabilities, answer the following questions:
- Are the
events that an applicant is dishonest and identified as a liar independent? Are these events mutually exclusive? - Can mutually exclusive events be independent events?
Consider the following steps in order to respond to the questions above
Step 1: Identify and define the two events and their complements. Correctly label the probabilities given using the defined events and their complements
Step 2. Make a Tree diagram. Compute the
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