QZ 1-C - ignition are stolen. On the other hand, only 0.2%...

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STAT 400 Fall 2011 Version C 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. On any given day, the parents in a certain family remember to feed the family dog with probability 0.80. The children remember to feed the dog with probability 0.55. 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 ) = 0.80 + 0.55 – 0.80 × 0.55 = 0.91 . OR P( Parents OR Children ) = 1 – P( nobody ) = 1 – 0.20 × 0.45 = 0.91 . b) (3) Find the probability that the dog would get fed exactly once on a given day. P( Parents only ) + P( Children only ) = 0.80 × 0.45 + 0.20 × 0.55 = 0.47 .
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2. (4) In Anytownville, 10% of the people leave their keys in the ignition of their cars. Anytownville’s police records indicate that 4.2% of the cars with keys left in the
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Unformatted text preview: ignition are stolen. On the other hand, only 0.2% of the cars without keys left in the ignition are stolen. Suppose a car in Anytownville is stolen. What is the probability that the keys were left in the ignition? P(Keys) = 0.10, P(Keys ' ) = 1 -0.10 = 0.90. P(Stolen Keys) = 0.042. P(Stolen Keys ' ) = 0.002. Need P(Keys Stolen) = ? Bayes’ Theorem: P(Keys Stolen) = ) Keys P(Stolen ) P(Keys Keys) P(Stolen P(Keys) Keys) P(Stolen P(Keys) | | | ' ' × + × × = 002 . 90 . 042 . 10 . 042 . 10 . × + × × = 0.70 . OR Stolen ' Stolen 0.042 ⋅ 0.10 Keys 0.0042 0.0958 0.10 Keys ' 0.002 ⋅ 0.90 0.0018 0.8982 0.90 0.0060 0.9940 1.00 P(Keys Stolen) = 0060 . 0042 . P(Stolen) Stolen) P(Keys = ∩ = 0.70 . OR P(Stolen) = 0.0042 + 0.0018 = 0.0060. P(Keys Stolen) = 0060 . 0042 . P(Stolen) Stolen) P(Keys = ∩ = 0.70 ....
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This note was uploaded on 02/15/2012 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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QZ 1-C - ignition are stolen. On the other hand, only 0.2%...

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