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Fall Quarter North Seattle Community College 2011 ELEMENTARY STATISTICS MATH 109 - Section 05 Chapter 3 and 4 - Quiz 2 2618 STUDENT NAME: QUIZSCORE: t:.sete f: DJe5>~ 25 24th Cl.Cd October 2011 __ Problem 1: 5 points Indentify the sample space and the number of elements inthe sample space of the probability experiment and determine the number of outcomes in the event. Draw a tree diagram. Experiment: Guessing the gender of the three children in a family Event: The family has two boys. I t:;l "nO o<., .: v.eJY., \~ .jvJ O!~_ '" I 1 B q~ ..; B G- B G- I E \-1 \' c;. B & ~ G- I ,-, G- (3 G - Problem 2: (7 points) A deck of cards has 52 cards with 13 hearts. A gambling game consists of a player drawing three cards without replacement. The required bet is $1000 i.e. you need $10 to buy into the game. The winnings depend on the number of hearts drawn out of the three cards. If you get no hearts you win $0, for 1 heart you receive $10, for 2 hearts you can win 20 and for all hearts you can win 500. 1. What 2. is the probability distribution for number of hearts drawn? What would be the average gain? 3. What is the variance and standard deviation for the gain? J.. r(J.)JJI he.oJ\..L:: d (CAvJ. \ ..; f\J4- he.M ~ :;..'!-.. X- I/ H 1\ \-t I 0 - -~i JJ f. -\0 e:« ) H >< Y--J1 (X--f\j2.. pc o'1f-1~5 I-Lt-t35 13· 563 ·'t_.~5S "t6 - o:t- -3-50 I.?- b<;S 5-431- ttl - "!-2>5 x{P{'Y' I 0 O-lf~5'3 :1. \0 o,13:n \-3++ Lt~O O'OIJ~ - - P rx~ 'Y. 1\ __, - 3 )L X 0 i- '2.-:;l G-'jdl 2 <: 5€;3 '_ ,._ 5' - 53 5- J_ -_ - LtS'6' 't3'! ).3b,b:t)-~b -x.) ( ~ - f'! ) - 2 I :,D S;J'41 i;:. 3 I 3'j - =+;;:1 - C) O-l.l ~5 I Jdt3S~ -...._ O-13l--=t- 3 0'0129 Problem 3: (5 points) Suppose that 60% of all people would like to see gun control laws strengthened. In sampling 10 people randomly (with replacement), let x represent the number of people who would like to see gun control laws strengthened. 1. What is the probability that at least 3 of the 10 people surveyed would like gun control strengthened? What is the mean for the number of people who would like gun control strengthened? 2. 3. What is the variance and standard deviation for the number of people who would like gun control strengthened? I) '1\:., 0 f ( )::'~"3 r flX- ) -;. - =- O' 6 0 \ - f C _ 0 )_ PlX-::IJ p.: . If) 0 C 10 I . ('x =- 0 J o O'bO O'bO xe s 9 -:. C>. Lf 0 I . P (x ::I ') D' 0' . F ( x -= ~ ') - 10-0 4-0 -ro ::. \0 -I [).~L)-"" .... ( I X lox '3 '. x 0' 6 0 _ - al 5" ~ 7(1 e Ct(l:: f\ \- D' 000\ p :: 10 v - CJ'" o· o \8 - . ~XSy~ 6 0 z: (. O' ..) YO' 000 ~ II ~. ')(0,3G" ~)(1'11 P('X.~ 3") -: o·D:)ol X c).00..31': I 3 =- Q. :p... ;Jb 0'0 -= () ,() I 8 001 - _..v , (J/l3 . v Problem 4: (8 points) Consider the sample space below. Each smiley face is an outcome in the sample space. Outcomes in the larger circle count as Event A Outcomes in the smaller circle count as event B. 1. What is the peA)? What is the PCB)? 2. What is the peA I B)? 3. What is the peA and B)? 4. Are A and B mutually exclusive events? Explain using probabilities. 5. Are A and B independent events? Explain using probabilities. \) '1)W :: \ 0 A ~ 5 pA)::;IO-5-:.2 10 'Di...J) : g::: r I.) 3 Dr B J :: II) 1.. : to 0.3