MATH
Exam I Solutions

# Probability and Statistics for Engineering and the Sciences (with Student Suite Online)

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Unformatted text preview: < EWﬁ Sou/110M? I {4613.) Iplay 1n a church softball league and, on the nights we play our team typically plays two games. W on a given night the chance we win our ﬁrst game is 0.60, the chance we win our second game is 0.65, and the chance that we win at least one game is 0.85. Hag ‘ F = we win our First game, and S = we win our Second game We the following: a. The chance we win both games. WW5) = me) + 145)- PCP/Ls) -.—9 Farms) ¢ {’(FM ww- Falls) 7 160+. 65"“ .7; = .1‘0 b. The chance we win only the ﬁrst game. r(Fn5’)=.z ' c.1‘he chance we win exactly one game; F/WsOUCS/IF'» ”" I’M/259+ {CS/1F!) —.— Kai-.25 = .45 Fm mam _; ed. Th: chance we win neither game. ﬂF’ns’): .15 _- l e. The chance we win the second game given that we win the ﬁrst game. V(5/F) = PZSAP) = ~7‘ -——-- E PCP) '6 3 2. (15 pts.) Tetrahedral dice (i.e. dice in the shape of a pyramid) have four faces that are equally likely to appear. Assume that when such a die is thrown, that you may get a 1, get a 2, get a 3, or get a 4. a. A single tetrahedral die is tossed 5 times. What is the chance of at least one 2 appearing? ”WWW. 2.) -,~ I~PL~0 2-) b. A pair of tetrahedral dice are thrown 6 times. What is the chance of at least one double 2 appearing? ”01' (ﬁbroid pace»: 2) =. 1.. POUO pauses. 7.) =— I" 72—; =‘.3ZI( 3. In the ‘Nebraska Pick 5 Lottery’ game you pick 5 numbers from 1 through 38. The amount you win depends on how many of your chosen numbers match the 5 eventually chosen as the winning numbers. Here is a payout schedule: —__ / a. (5 pts.) In one play, what is the chance that you win the Jackpot? You may leave your answer in temts of W binomial coeﬂicients. L.” PM)!» M07“) 5 ( 3;) , ooeoolqﬁ 2,} b. (10 pts.) In one play, what is the chance that you have gross winnings of \$9? Again, you may leave your answer in terms of unevaluated binomial coeﬁ‘icients. 5. 5 3 V/Wis \$7) = (3)< if) (iv/mum, 3? <5 3“ .0105L 3 4. (2096.) Suppose, among SDSM&T students, that 5.00% of men and 1.00% of women are color-blind'. Also suppose that 65% of SDSM&T students are male and 35% of SDSM&T students are female. A single SDSMT student is chosen at random. 3. What proportion of SDSM&T students are color-blind? C : (Mar—Hm; [‘1 -; Mlc/ F 5 Panic {7(6): V(C/I‘1)I’(W)+ V(¢IF)P(F) = 6052665)+ 60063;) = .1934 b. Given the student is color-blind, what is the chance of this person being male? Wide)" V(6/m) WM) Flo) : (.05) (.55) ' . 5. (15 pts.) Some counting problems. Don’t waste time simplifying answers (expressions involving binomial coeﬁ‘icients and/or powers may be leﬁ Mevaluatg). a. Suppose a certain password must be 8 characters long. Also suppose that each character may be either a lower—case alphabetical letter (26 of these, of course) or a digit from 0-9 (10 of these, of course). . How many passwords are possible? 34 3: 34 34 253 (agraué‘ fwwdt‘pg b. A motel I went to a few years ago gave out keys to rooms which consisted of plastic cards in which 25 positions could either left alone or have circles punched out of them. How many key settings could be handled by these cards? 22—17.. 2 '27: '15 225 K 61! Simo'a; c. {an coach/manager of a softball team. I have a roster of 19 players but can only place 10 people in the ﬁeld at I time (pitcher, catcher, 1“, 2'“. shortstop, 3'“. left ﬁeld, center ﬁeld, right ﬁeld, and “rover”). In how many different ways can I choose 10 of my 19 players and arrange them in the ﬁeld? W W P65! 176‘ 5M0? V1?” 10 PLMEM Fa”, ...
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