Question

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. Find the probability of observing no positive reading if all suspects plead innocent and are telling the truth.

Answer 1

$P(\frac{Test \;negative}{Truth}) = 1 -P(\frac{Test \;positive}{Truth}) \\ = 1 -0.10 \\ = 0.90 \\ P(\frac{all\;five\;results\;are\;test\;negative}{All\;suspects \;telling\;truth}) = \\ = p^5 \\ = 0.9^5 \\ = 0.591$