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k.aspx?homeworkld-4540759068questionid 1&flushed-false;&cld-4748265;&icenterwinsyes; 201810-STA307-E01-CRN12654-Robert FEGHALI-MF11:00-12:15 Homework: STA307- Homework2 Score: 0 of 1 pt 2.R.103 201810 1 of 32 (0 complete) HW Score: 0%, 0 of 32 pts Question Help * A t uth serum has the property that 91% of the guilty suspects are property judged while, of course, 9% of the guity suspects are improperly found innocent On the other hand nnocent suspects are misudged 1% of the time. If the suspect was selected from a group of suspects of which only 9% have ever committed a crme, and the serum indicates that he is guilty, what is the probability that he is innocent? The probability that the suspect is innocent is Round to four decimal places as needed) u)More Enter your answer in the answer box and then click Check Answer All parts showingExplanation / Answer
Let A be the event of a person being guilty and B be the event of being correctly judged.
P(B|A) = 0.91 P(B'|A) = 0.09
P(B'|A') = 0.01
P(A) = 0.09 => P(A') = 1 - 0.09 = 0.91
=> P(B A) = P(B|A) P(A) = 0.91 * 0.09 = 0.0819
P(B' A') = P(B'|A') P(A') = 0.01 * 0.91 = 0.0091
=> P(A U B) = 1 - P(B' A') = 1 - 0.0091 = 0.9909
P(B) = P(A U B) + P(B A) - P(A)
= 0.9909 + 0.0819 - 0.91
= 0.1628
P(B') = 1 - P(B) = 1 - 0.1628 = 0.8372
P(A'|B') = P(B' A') / P(B')
= 0.0091 / 0.8372
= 0.0109.
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