Question

A polygraph test is sometimes used to detect if someone is lying, but it is generally not admissible in court because of its dubious accuracy. A polygraph test is given to 98 people, and the test is wrong for 24 of them. What is the empirical probability that the polygraph test is wrong for a randomly chosen person? What is the probability that it is right?

a) The empirical probability that the polygraph test is wrong is 24/98.
b) The probability that the polygraph test is right is 74/98.
c) The empirical probability that the polygraph test is wrong is 74/98.
d) The probability that the polygraph test is right is 24/98.

Answer 1

The empirical probability that the polygraph test is wrong for a randomly chosen person is 24/98, which simplifies to 12/49. The probability that the polygraph test is right is 74/98, which simplifies to 37/49.

Step-by-step explanation:

To find the empirical probability that the polygraph test is wrong for a randomly chosen person, we take the number of times the test was wrong and divide it by the total number of people tested. The test was wrong for 24 out of 98 people, so the empirical probability is 24/98.

Similarly, to find the probability that the polygraph test is right, we subtract the number of incorrect results from the total number of people tested to find the number of correct results. Since the test was wrong 24 times, it was right for the remaining 98 - 24 = 74 people. Therefore, the probability that the polygraph test is right is 74/98.

Now we simplify the fractions: 24/98 simplifies to 12/49, and 74/98 simplifies to 37/49. Hence, the correct answers are:

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