Answer:

Explanation:
Let
be the probability of lying an applicant, so,
.

Any applicant will either lie or will tell the truth.
Let
be the probability of telling the truth, so,


As for every applicant
, so this is Bernoullies trials, for which
the probability of success of exactly
times of an event out of
trials is
.
Now, let
be the event of at least one of the applicants is lying out of
applicants, here the total number of applicants,
.
So,

This is equivalent to
as
![[P(x=0)+P(x=1)+ P(x=2)+\cdots+ P(x=11)=1]](https://img.qammunity.org/2021/formulas/mathematics/college/a1akvywdy0tgqkdojogaxc0vwcjispbbji.png)
Now, from equation (iii),
[from equations s (i) and (ii)]

(approx)

Hence, the probability that the lie detector indicates that at least one of the applicants is lying is
