Respuesta :
Answer:
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
The probability of that Jones is lying is [tex]\frac{6}{7}[/tex] .
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,
[tex]P=0.8*0.6=0.48[/tex]
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,
[tex]0.2*.0.4=0.08[/tex]
Total probability of outcome being a lie is,
[tex]0.48+0.08=0.56[/tex]
Thus, Probability of Jones telling lie is, [tex]=\frac{0.48}{0.56} =\frac{6}{7}[/tex]
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