# Exam1Aans - Exam 1 1(Version A white(Answers The population...

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Exam 1 ( Version A – white ) ( Answers ) 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) (3) You meet a Lilliputian with blue eyes. What is the probability that he is a Little-Endian? P( Little | Blue ) = 20 . 0 096 . 0 ) Blue ( P ) Blue Little ( P = = 0.48 . c) (3) 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 .

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2. (3) How many ways are there to rearrange letters in the word MISSISSIPPI ? 11 letters: 4 I , 1 M , 2 P , 4 S . ! ! ! ! ! 4 2 1 4 11 = 34,650 . OR 11 C 4 7 C 1 6 C 2 4 C 4 = 330 7 15 1 = 34,650 . 3. (4) In order to create more room in his freezer, Alex took all pizza pockets out of the boxes, but he forgot to label them. He only remembers that 5 are ham and cheese, 7 are pepperoni pizza, and 4 are Philly steak. When a few of his friends drop over for a game of poker, Alex decides to serve pizza pockets. If he selects 5 pockets at random, what is the probability that 2 of them are ham and cheese and 3 are
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Exam1Aans - Exam 1 1(Version A white(Answers The population...

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