QUIZ 1-3 - What is the probability that he is a...

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STAT 400 Spring 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. The population of Lilliput is divided into Little-Endians and Big-Endians based on which end of a boiled egg they believe should be opened. Suppose that 60% of Lilliputians are Little-Endians, and 40 % are Big-Endians. Suppose also that 16% of Little-Endians and 26% of Big-Endians have blue eyes. P( Little ) = 0.60, P( Big ) = 0.40, P( Blue | Little ) = 0.16, ( 16% of Little-Endians have blue eyes ), P( Blue | Big ) = 0.26. ( 26% of Big-Endians have blue eyes ). a) (4) What proportion of Lilliput population have blue eyes? Blue Blue ' Little 0.60 0.16 0.096 0.504 0.60 P( Blue | Little ) = 0.16 Big 0.40 0.26 0.104 0.296 0.40 P( Blue | Big ) = 0.26 0.20 0.80 1.00 OR P( Blue ) = P( Little ) P( Blue | Little ) + P( Big ) P( Blue | Big ) = 0.60 0.16 + 0.40 0.26 = 0.096 + 0.104 = 0.20 . b) (2) You meet a Lilliputian with blue eyes.
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Unformatted text preview: What is the probability that he is a Little-Endian? P( Little | Blue ) = 20 . 096 . ) Blue ( P ) Blue Little ( P = ∩ = 0.48 . 1. (continued) c) (2) What is the probability that a Lilliputian is a Little-Endian, if his eyes are not blue? P( Big | Blue ' ) = 80 . 296 . ) Blue ( P ) Blue Big ( P = ∩ ' ' = 0.37 . d) (2) The first democratically elected Lilliputian president is a Little-Endian with blue eyes. His first day in office he proposed a tax break for Lilliputians who are either Little-Endians or have blue eyes, or both. What proportion of the Lilliput population would receive a tax break under his proposal? P( Little ∪ Blue ) = P( Little ) + P( Blue ) – P( Little ∩ Blue ) = 0.60 + 0.20 – 0.096 = 0.704 . OR P( Little ∪ Blue ) = P( Little ∩ Blue ) + P( Little ∩ Blue ' ) + P( Big ∩ Blue ) = 0.096 + 0.504 + 0.104 = 0.704 . OR P( Little ∪ Blue ) = 1 – P( Big ∩ Blue ' ) = 1 – 0.296 = 0.704 ....
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This note was uploaded on 11/28/2011 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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QUIZ 1-3 - What is the probability that he is a...

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