Math 240 midterm solutions, Exams of Mathematics

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PROBABILITY AND STATISTICS FOR ENGINEERS MIDTERM 1 : CVE 308 Name: Se lutions Signature : Code Last Name: Acad. Year: 2019-20 Semester : Fail Date 03.11.2019 | Student ID: Time 2 10:40 Duration : 110 min 7 QUESTIONS ON 4 PAGES TOTAL 100 POINTS PL. (a5yP2. (25)]PS. (25))PS. (25) Pistar (100) PlTest N [Event Y= Yo + Alas 1. Use the following data to fill in the table of probabilities and answer the questi Below. ? ’ — A test for an cvent has a false positive Prob. l Test Y ‘Test Total rate of 5 Plroer ¥ Levent W) = Yo | Bveat || 78,5 |||C%oo ))|| — The test has Boe ne} ative 1 te of a ov, est Nf Even = 2 G sy — Prior to testing, the probability of the Event N Coo I vo y fe event occurring is estimated to be 4 We se ° Total % > 1 P(Event y= No ie : What is the probability the event occurring and the test result. being positive? P(Event V wd Test Y) = e What is the probability of the test being pos- itive if the event occurred? P (tess Y | Event Y)= Ko —_—- 4A y No This is — l= P (est Wf Event ¥) = ms) e What is the probability of the event having occurred if the test result was positive? P(Event ¥ | Test ¥) = Boo 3 ft WY = 4 22 PCtest VleverN)= Yio « What is the probability the event occurring or the test result being positive? PCBent y or Test XY = 1- %o = e What is the probability of a positive result from the test? : PC tet y) = 4 * What is the probability of the event, having occurred if the test result was negative? P (Event Y | Test N) = Li’. Yoo 2 sl si se joo