A lie-detector works correctly with 80% probability when the person is lying, and with 90% probability when the person is not. Assume that in a given court, typically 70% of the people who have to be tested with the lie-detector do not say the truth. On the long run, which percentage of time does the lie detector make a mistake?

the time percentage is 17%

Step-by-step explanation:

The computation of the time percenatge in the case when the detector lie and done with the mistake is as follows:

L denotes the event  in which a person is lying.

NL denotes the event in which a person is not lying.

C denotes the event in which that lie detector works correctly

NC denotes the event in which  lie detector is not working correctly

Now

P(C|L) =0.8

And,

P(NC|L) is

=1 - .8

= 0.2

P(C|NL) =0.9

P(NC|NL) is

= 1 -.9

=.1

P(L) = 0.7

P(NL) is

= 1 - .7

= .3

Now

P(NC) =P(NC|L) × P(L) + P(NC|NL) × P(NL)

=. 2 × .7 + .1 ×.3

=. 14+.03

= 0.17

Hence, the time percentage is 17%