Dalgliesh the detective fancies himself a shrewd judge of human nature. In careful tests, it has been discovered that he is right 80 percent of the time about whether a suspect is lying or telling the truth. Dalgliesh says that Jones is lying. The polygraph expert, who is right 100 percent of the time, says that 40 percent of the subjects interviewed by Dagliesh are telling the truth. What is the probability that Jones is lying?

The probability of that Jones is lying is .

Probability is defined as, divide favourable outcomes by total outcomes.

First case:

Probability that Jones tells lies is = 0.6

Probability that Dalgliesh analyses it correctly is, =  0.8

Therefore,  the probability that Dalgliesh correctly analyses that Jones is telling lies is,

Second case :

Probability that Jones tells truth is, =  0.4

Probability of Dalgliesh  analyses it incorrectly that Jones tells truth is,

                                                = 0.2

So, Probability that Dalgliesh analyses Jones truth as a lie is,

Total probability of outcome being a lie is,

Thus, Probability of Jones telling lie is,  

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The probability that Jones is lying is 6/7

Step-by-step explanation:

First we will list out 2 different cases when the outcome is a lie

1.probability that Jones tells lies is = 0.6 and probability that dalgiliesh analyses it correctly is 0.8

So the probability that dagliesh correctly analyses that he is telling lies is 0.8*0.6=0.48

2.Probability that Jones tells truth is 0.4 and if dagliesh analyses it incorrectly (which has a probability of 0.2) the outcome(as analysed by dagiliesh) is a lie

So probability that dagliesh analyses Jones truth as a lie is 0.2*.0.4=0.08

Total probability of outcome being a lie is 0.48+0.08=0.56

But we need the probability of Jones actually saying a lie which is nothing but 0.48/0.56= 6/7

a. is correct