Answer:

Step-by-step 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://tex.z-dn.net/?f=%5BP%28x%3D0%29%2BP%28x%3D1%29%2B%20P%28x%3D2%29%2B%5Ccdots%2B%20P%28x%3D11%29%3D1%5D)
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 