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Experience has shown that a certain lie detector will show a positive reading (indicates a lie) 10% of the time when a person is telling the truth and 95% of the time when a person is lying. suppose that a random sample of 5 suspects is subjected to a lie detector test regarding a recent one-person crime. then the probability of observing no positive reading if all suspects plead innocent and are telling the truth is

Respuesta :

In this case, there are 5 suspects and all are plead innocent. Assuming that only 1 person guilty, then it should be 1 person lying that get negative reading and 4 people telling the truth that get a negative reading. The chance for negative reading is:
when telling lie= 100-95%=6=5%
when telling truth= 100-10%=90%

Then the chance would be: 5%* (90%^4)= 3.2805%

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