MATH SOLVE

2 months ago

Q:
# An article states that false-positives in polygraph tests (tests in which an individual fails even though he or she is telling the truth) are relatively common and occur about 10% of the time. Suppose that such a test is given to 10 trustworthy individuals. (Round all answers to four decimal places.) What is the probability that all 10 pass?

Accepted Solution

A:

Answer:0.3487 or 34.87%Step-by-step explanation:If false-positives occurs about 10% of the time, it means that polygraph tests are accurate around 90% of the time.
That is, the probability that the polygraph does not give a false-positive is 0.9
Since the result given by the polygraph to a given question is independent from the responses to any previous question (or it should be), then the probability that the polygraph does not give a false-positive 10 times in a row with 10 people that are telling the truth is
[tex]\large (0.9)^{10}=0.3487[/tex] or 34.87%