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# QZ 1-D - with probability 0.85 The children remember to...

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STAT 400 Fall 2011 Version D Name ANSWERS . Quiz 1 (10 points) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. (4) A chemical plant has an emergency alarm system. When an emergency situation exists, the alarm sounds with probability 0.95. When an emergency situation does not exists, the alarm system sounds with probability 0.02. A real emergency situation is a rare event, with probability 0.4%. Given that the alarm just sounded, what is the probability that a real emergency situation exists? P ( A | E ) = 0.95, P ( A | E ' ) = 0.02, P ( E ) = 0.004. Need P ( E | A ) . P ( E | A ) = ) E A P( ) E P( ) E A P( ) E P( ) E A P( ) E P( | | | ' ' × + × × = 02 . 0 996 . 0 95 . 0 004 . 0 95 . 0 004 . 0 × + × × = 01992 . 0 00380 . 0 00380 . 0 + = 02372 . 0 00380 . 0 0.1602 . ( Bayes’ Theorem ) 2. On any given day, the parents in a certain family remember to feed the family dog
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Unformatted text preview: with probability 0.85. The children remember to feed the dog with probability 0.60. Assume independence. a) (3) Find the probability that on a given day either the parents or the children (or both) would remember to feed the dog. P( Parents OR Children ) = P( Parents ) + P( Children ) – P( Parents AND Children ) = 0.85 + 0.60 – 0.85 × 0.60 = 0.94 . OR P( Parents OR Children ) = 1 – P( nobody ) = 1 – 0.15 × 0.40 = 0.94 . b) (3) Find the probability that the dog would get fed exactly once on a given day. P( Parents only ) + P( Children only ) = 0.85 × 0.40 + 0.15 × 0.60 = 0.43 ....
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