To improve poultry management and protect public health, researchers have develo

Question

To improve poultry management and protect public health, researchers have developed a prototype test that can be used to detect a lethal poultry virus. During humid and hot weather, the lack of aeration in poultry houses creates favorable conditions for the virus. Based on preliminary results, researchers have found that:

If a hen is sick, the test will be positive with a probability of 95%

If a hen is not sick, the test will produce a false positive with a probability of 15%.

Questions:

a) What is the probability that a hen is infected with the virus if the test shows positive results?

b) What is the probability that a hen will test positive when it is not infected with the virus?

c) What is the probability that a hen is infected with the virus if the test shows negative results?

d) What is the probability that a hen will test negative when it is not infected with the virus?

Explanation / Answer

suppose the probbaility of hen being sick = p

probability that test shows positive result = (p * 0.95 + (1-p) * 0.15)

a) What is the probability that a hen is infected with the virus if the test shows positive results?

= p * 0.95 / (p * 0.95 + (1-p) * 0.15)

b) What is the probability that a hen will test positive when it is not infected with the virus?

= 0.15

c) What is the probability that a hen is infected with the virus if the test shows negative results?

= p * (1-0.95)/ ( p * (1-0.95) + (1-p) (1-0.15))

= p * 0.05 / (0.05 p + 0.85(1-p) )

d) What is the probability that a hen will test negative when it is not infected with the virus?

=0.85

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

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