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Correct answer is C.

Let us use tree diagram to solve this.

Let A be the event define people telling the truth.

so, P(A)=0.9

A lie detector confirms correctly a person telling lie or truth with probability 0.8.

The tree diagram looks like this,

So, now probability that lie detector confirms true =probability person telling truth and lie detector confirm it true or probability that person telling lie and lie detector confirms true

$P(LCT)=P(A)*P(\frac{LCT}{A})+P(\bar{A})P(\frac{LCT}{\bar{A}})$

=$0.9*0.8+0.1*0.2$

=$0.74$

We have to find given lie detector telling truth, probability that the person actually telling the truth which is

$P(\frac{A}{LCT})=\frac{P(A)\cap P(LCT)}{P(LCT)}=\frac{0.9*0.8}{0.74}=\frac{36}{37}$