MA201 A - Statistics for Behav\'l &Health; Sciences Patricla RyanI 2/19/18 1:30
ID: 3046806 • Letter: M
Question
MA201 A - Statistics for Behav'l &Health; Sciences Patricla RyanI 2/19/18 1:30 PM Homework: Section 3.2 Homework Score: 0.5 of 1 pt 32.37 Save 13 of 13 (13 complete) HW Score: 96.15%, 12.5 of 13 pts Question Help * Acertain virus infects one in every 150 people. A test used to detect the virus in a person is positive 90% of the tirne when the person has the virus and 10% ofthe time when the person does not have the virus. is 10%rosult is called a false positive. Let Abete event "the person is infected and B bethe eventhe 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 Click 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.) Enter your answer in the answer box and then click Check Answer Clear All Check Answer remaining ExcelExplanation / Answer
a) P(A) = 1/150 = 0.007
P(B) = P(B | A) * P(A ) + P(B | A') * P(A')
= 0.9 * 0.007 + 0.1 * 0.993
= 0.1056
P(A | B ) = P(B | A) * P(A)/(P(B )
= 0.9 * 0.007/0.1056
= 0.06
b) P(A'|B') = P(B'|A') * P(A')/P(B')
= 0.9 * 0.993/(1 - 0.1056)
= 0.999
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