Respuesta :
Answer:
The value of Q is 350.
Step-by-step explanation:
Denote the events as follows:
X = the test is positive
Y = the test is negative
A = the person is telling the truth
B = the person is telling a lie.
It is provided that:
P (B ∩ X) = 0.90
P (A ∩ Y) = 0.50
Then:
P (B ∩ Y) = 1 - P (B ∩ X) = 1 - 0.90 = 0.10
P (A ∩ X) = 1 - P (A ∩ Y) = 1 - 0.50 = 0.50
To test the accuracy of lie-detector a police officer tests 1000 suspected criminals.
It is assumed that 700 per 1,000 suspected criminals tell the truth during polygraph tests.
The table needed to be completed is:
Truth (A) Lie (B) TOTAL
Positive (X) Q __ __
Negative (Y) __ P __
TOTAL __ __ __
For the 1000 suspected criminals selected complete the table as follows:
Given:
Truth (A) Lie (B) TOTAL
Positive (X) Q __ __
Negative (Y) __ P __
TOTAL 700 300 1000
n (A ∩ X) = P (A ∩ X) × n (A)
= 0.50 × 700
= 350
n (A ∩ Y) = P (A ∩ Y) × n (A)
= 0.50 × 700
= 350
n (B ∩ X) = P (B ∩ X) × n (B)
= 0.90 × 300
= 270
n (B ∩ Y) = P (B ∩ Y) × n (B)
= 0.10 × 300
= 30
n (X) = n (B ∩ X) + n (A ∩ X)
= 270 + 350
= 620
n (Y) = n (B ∩ Y) + n (A ∩ Y)
= 30 + 350
= 380
Complete table is:
Truth (A) Lie (B) TOTAL
Positive (X) Q = 350 270 620
Negative (Y) 350 P = 30 380
TOTAL 700 300 1000
Thus, the value of Q is 350.
