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Solutions - Math 381 Probability Statistics I Name Vr:~Jf...

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- Math 381 Probability & Statistics I Name: Vr:::~Jf o,J :J- EXAM 1 Fall 2005 RWJ Instructions: . One page of notes and calculator allowed (but nothing else) . Please show work/reasoning for (partial) credit . Read questions carefully . Note point values on questions . If you haveextra time, check over answers beforeturning in your exam . Note any writing on the blackboard pertaining to the exam . Good luck! \', PLEASANT foLk, YES" £V£N - o- r. THOSE STATI - \HE: M£At-J STI ClANS! STATISTICIAN IS ~fTE.NIC6, I "::: S~~~:=~}~~~~~ "- ' , :: " ' I -, , -- - "~- .,.,.. . ~- -~ / 1. /30 2. /22 3. /25 4. / 7 5. /12 6. / 7 /103 (maximum score of 100is possible) )
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i ! 1. (30 pts.) Your instructor played on a softball team this past summer where we played two games each night we played. Suppose that we won the first game 35% of the time (i.e. a probability of 0.35), the second game 75% of the time, and both games 25% of the time. Determine each of the following: a. The chance we won at least one game. f(f~5) = ./O..f-.Z5-1-.>D :[email protected] b. The chance we won only the first game 5 f f( r=~ ..5 () =-~ f;:. ()),; fir?f- C;-(J.~ S:.. .,..54.C e;.-I\.L 1\ c. The chance we won exactly one game / f((r-4~S')P"2 (?/~~)) & d. The chance we won the second game given we won the first game. t ( 5 / F ) .: ~~-~~.:.):: .:.:!. ../I""'~~:\ '\ p ( P) . 'J ~ \',2 ~~~,) 2 i ! I "
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2. (22 pts.) In the Minnesota"Gopher 5" Lottery one chooses 5 numbers from the field 1 through47. The game costs $1 to play. Here is a table of an individual's (gross) winnings by the number of matches they have: Numberof Matches Winnings ... . T1.1 5 of 5 numbers Jackpot (starts at $100,000) 4 of 5 numbers $500 3 of 5 numbers $15 2 of 5 numbers $1 a. What is the chance of winning the Jackpotin a single play? Express your answer in termsof binomial coefficient(s). - ( f (fA)J~ I av~+') ': ~-- ( ~7) b. What is the chance of winning $15 (i.e. that you have net winnings of $14)? Express your answer in termsof binomial coefficient(s).
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