Suppose a certain sports league has a strict no drinking policy. The 3,000 playe
ID: 3039251 • Letter: S
Question
Suppose a certain sports league has a strict no drinking policy. The 3,000 players of the league are given a polygraph during which they are asked whether they have taken a drink in the last three months. All of them deny drinking but in actually 2% of the players are delinquent. Use the table below to answer the following questions. This table assumes that a polygraph is 90% accurate.
Player Is Lying
Player Is Truthful
Total
Polygraph Finds Player Lying
54
294
348
Polygraph Finds Player Truthful
6
2,646
2,652
Total
60
2,940
3,000
Suppose the polygraph results found the player is lying. What is the chance that he/she really is lying?
____________%
What is the chance the polygraph results finds the player is lying, given that the player is lying?
____________%
Suppose polygraph results found player truthful. What is the chance that he/she is lying? Give this answer as a percentage rounded to two decimal places.
____________%
What is the chance the polygraph results finds the player lying, given that the player is truthful? Answer with a percentage rounded to the nearest tenth.
____________%
Player Is Lying
Player Is Truthful
Total
Polygraph Finds Player Lying
54
294
348
Polygraph Finds Player Truthful
6
2,646
2,652
Total
60
2,940
3,000
Explanation / Answer
(1). Polygraph finds player lying (total) = 348
In reality player is lying = 54
So, when the polygraph results found the player is lying. The chance that he/she is really lying = (54/348)×100
= 15.51%
(2). Player is lying (total) = 60
Polygraph results found the player is lying = 54
So,. When a player is lying, the chance of polygraph results found the player is lying = (54/60)×100
= 90%
(3). Polygraph finds player truthful (total)= 2652
In these player lying = 6
So, when polygraph finds player truthful, the chance that he/she is lying = (6/2652)×100
= 0.22%
(4). Player is truthful (total) = 2940
In these polygraph finds the player lying = 294
So, when a player is truthful, then the chance of polygraph finds the player lying = (294/2940)×100
= 10%
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