A small portable water testing machine permits a quick, easy, inexpensive, on-si

Question

A small portable water testing machine permits a quick, easy, inexpensive, on-site testing of samples but is not as reliable as laboratory testing in two ways. First it fails to detect the contamination in 20% of the samples that are know to be contaminated ( "missed detection" ) and second it also gives a false indication of contamination in 10% of the samples that are known to be uncontaminated ( "false positive" )
What is the probability that a randomly selected sample taken from the polluted area, when tested with the portable machine will be indicated as being contaminated?

Explanation / Answer

Event T : Water testing machine gives positive test for contamination.
Event C : Water is actually contaminated.

Given:
Missed Detection - P(Tc | C) = 0.20
False Positive - P(T | Cc) = 0.10
To find:
Probability that a randomly selected sample taken from the polluted area tests positive for contamination with the portable machine.
Since the sample is taken from polluted area , water is contaminated.
To find: P(T | C) = 1 - P(Tc | C) = 1 - 0.20 = 0.80

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.