
No (Did Not Lie)

Yes (Lied)



Positive test results

1717

4444


Negative test results

3535

1414

Concept of probability:
Probability deals with the likelihood of occurrence of a given event. The probability value lies between 0 and 1. An event with probability 1 is considered as certain event and an event with probability 0 is considered as an impossible event. The probability of 0.5 infers of having equal odds of occurring and not occurring of an event.
The general formula to obtain probability of an event A is,
P(A) = (number of favourable elements for event A)/(Total number of elements in the sample space).
The basic properties of probability are given below:
Find the probability that the randomly selected polygraph test subject was not lying:
Given that from the sample data of polygraph tests, one test subject is randomly selected.
The total number of test subjects that are not lying is, the sum of test subjects that are not lying in positive results tests and negative results tests.
That is, the total number of test subjects that are not lying 1,717 + 3,535 = 5,252.
The total sample size is 1,717 + 3,535 + 4,444 + 1,414 = 11,110.
The probability that the randomly selected polygraph test subject was not lying is obtained as 0.473 from the calculation given below:
Check whether the probability that the randomly selected polygraph test subject was not lying is close to 0.445:
The probability that the randomly selected polygraph test subject was not lying is 0.47...
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