Question

Some employers use lie detector tests to screen job applicants. Lie detector tests are not completely reliable. Suppose that in a lie detector​ test, 65% of lies are identified as lies and that​ 14% of true statements are also identified as lies. A company gives its job applicants a polygraph​ test, asking​ "Did you tell the truth on your job​ application?". Suppose that​ 93% of the job applicants tell the truth during the polygraph test. What is the probability that a person who fails the test was actually telling the​ truth? Round to three decimal places as needed.​ (Hint: divide the probability that a person told the truth and failed the test by the probability that a person failed the​ test.)

Answer 1

Answer:

The probability that a person who fails the test was actually telling the​ truth is 0.741

Step-by-step explanation:

For calculate this probability is necessary to divide the probability that a person told the truth and failed the test by the probability that a person failed the​ test.

Lets call P1, the Probability that a person told the truth and failed the test. It is the multiplication of:

P1 = 0.93*0.14 = 0.1302

Where 0.93 is the percentage of jobs applicants who tell the truth and 0.14 is the proportion of true statements that are identified as lies.

Let's call P2, the probability that a person failed the​ test. This probability is calculated in two parts:

• The probability that a person told the truth and failed the test: This is the same probability P1.
• The probability that a person didn't told the truth and failed the test: This probability is calculate as:

        0.07*0.65=0.0455

Where 0.07 is the percentage of jobs applicant who didn't tell the truth and 0.65 is the proportion of lies that are identified as lies.

So, P2 is the sum of the 2 cases and it is:

P2=0.1302+0.0455=0.1757

Then the probability that a person who fails the test was actually telling the​ truth is:

P=P1/P2

P=0.1302/0.1757

P=0.741

Answer 2

Probability means possibility. It deals with the occurrence of a random event. The probability that a person who fails the exam is telling the truth is 0.741.

What is probability?

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

% of lies are identified as lies = 65%

% of true statements are also identified as lies= 14%

% of the job, applicants tell the truth during the polygraph test= 93%

% the probability that a person who fails the test was actually telling the​ truth = ?

To compute this probability, divide the probability that a person revealed the truth and failed the exam by the likelihood that a person failed the test.

Let us refer to P as the probability that a person stated the truth yet failed the exam. It is the result of multiplying:

$P_1 = 0.93 \times 0.14 = 0.1302$

Where 0.93 represents the proportion of job candidates that speak the truth and 0.14 represents the fraction of truthful claims that are detected as falsehoods.

P₂ is the probability that a person failed the test. This probability is divided into two parts:

1. The probability that a person told the truth and failed the test: This is the same probability P₁.

2. The probability of those who didn't tell the truth and failed the test will be p'

     

$\rm p'= 0.07 \times 0.65=0.0455$

The percentage of jobs applicant who didn't tell the truth = 0.07

The proportion of lies that are identified as lies. = 0.65

P₂ is the sum of two cases then

$\rm P_2=0.1302+0.0455 \\\\\rm P_2=0.1757$

The probability of those who fail the test but tell the​ truth will be;

$\rm p= \frac{p_1}{p_2}$

$\rm p= \frac{0.1302}{0.0455}\\\\\\\rm p=0.741$

Hence the probability that a person who fails the exam is telling the truth is 0.741.

To learn more about the probability refer to the link;

https://brainly.com/question/795909