Homework: it 3: HW 3.2 Score: 0.5 of 1 pt 10 of 12 (1 3.2.37 A certain virus inf
ID: 3047459 • Letter: H
Question
Homework: it 3: HW 3.2 Score: 0.5 of 1 pt 10 of 12 (1 3.2.37 A certain virus infects one in every 250 people. A test used to detect the virus in a person is positive 70% of the time when positive.) Let A be the event tthe person is infected" and B be the event "the person tests positive." (a) Using Bayes Theorem, when a person tests positive, determine the probability that the person is infected. b) Using Bayes Theorem, when a person tests negative, determine the probability that the person is not infected. 1Click the icon to the right to review Bayes Theorem. (a) The probability that a person is infected when a person tests positive is Do not round until final answer. Then round to three decimal places as needed.)Explanation / Answer
P(the person is infected) = 1/250 = 0.004
P(test positive) = 0.004 * 0.7 + 0.996 * 0.05 = 0.0526
a) P(infected | test positive) = P(positive | infected) * P(infected)/P(test positive)
= 0.7 * 0.004 /0.0526 = 0.053
B) P(not infected | test negative) = P(test negative | not infected) * P(not infected)/P(test negative)
= 0.95 * 0.996 /(1 - 0.0526)
= 0.95 * 0.996/0.9474
= 0.9987
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