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1 USAestprep, Inc. \JSf~~Jp Analytic Geometry EOC Quiz Answer Key Statistics and Probability (MCC9-.S.ID.6a) Fit A Function o Data, (MCC9-.S.CP.l) Events And Outcome Sets, (MCC9-.S.CP.) Independent Events, (MCC9-.S.CP.) Conditional Probability, (MCC9.S.CP.) wo-way Frequency ables, (MCC9.S.CP.S) Everyday Examples, (MCC9-.S.CP.6) Find Conditional Probability, (MCC9.S.CP.7) Addition Rule Student Name: eacher Name: Keith Simmons Date: Score: )... 0 t! B Number of Gallons of Gas 0 he graph displays the total cost when buying gas by the gallon. Which statement best describes the relationship between cost and amount of gas purchased? />:) he more gas you buy, the more it costs. he more gas you buy, the Less it costs. he Less gas you buy, the more it costs. It costs the same no matter how much gas you buy. Since both the x and yvalues are increasing the relationship is positive. herefore the correct statment is the more gas you buy, the more it costs odules/qui z _factory/key. php /8

2 9/0 ) USAestprep,lnc. H Start H H ( ) ' ' i: ;;:' G) ~--H ;,.:; coin times. According to the tree diagram, how many possible outcomes exist? 6 8 he solution is 8. he 8 possibilities are as follows: HHH, HH, HH, H, HH, H, H,. ) 7PlumoV?WthefSofa<"""" Hantwood:... -~ LCD \f... ~ _ ~Plasma lv Cwtll Sofa ~ LCD V Pla-sma V? Leather Sofa lllo ~ \ LCD V ~ Cloth Sofi? Plat.ma V 'J. LCD V /'l Plasma V ;::; L&ather So-fa '<...~::: Carpet('. LCD V o;. c;,piasma V Cloth Sofa <:; ". LCD V Chris and Hillary are remodeling their family room. hey are deciding on the flooring, sofa and V. How many possible combinations are shown in the tree diagram? 0 q he solution is. he solution can be found by counting the choices or multiplying the choices for each category ()()=. / _factory!key.php 8

3 9/0 USAestprep, lnc. ) Jane has blue marbles, red marbles, and yellow marbles in a bag. Jane will randomly pick one marble from the bag. What is the probability the marble will be yellow? 7 9 he probability that John will get a yellow marble is :9. here are 9 total marbles and of them are yellow. ) Michelle draws a card from a standard deck of cards. She replaces the card and draws a second card. What is the probability that she draws a red card and then a black card? 6 6 he solution is!_ Since the two events are independent, the outcome of one event does not affect the outcome of the other event. o find the compound probability we multiply the probabilities of the two events. he probability of drawing a red card is 6 or.!:. he same is true for the probability of drawing a black card.. - = ) Michelle draws a card from a standard deck of cards. She replaces the card and draws a second card. What is the probability that she draws a Heart and then a Spade? 6 6 he solution is _.!_.Since the two events are independent, the outcome of one event does not affect the outcome of the other event 6 o find the compound probability we multiply the probabilities of the two events. he probability of drawing a Heart is or I.. he same is true for the probability of drawing a Spade..!: = _.!:_ 6 tvj.p:/lww'w.usatestprep.com/m odul es/quz _factory/key.php 8

4 9/0 7) Which event includes an example of a dependent event? A coin is flipped. he result is recorded. he coin is then flipped a second time. A die is rolled. he result is recorded. he die is then rolled a second time. A card is drawn from a standard deck of cards. he card is replaced and a second card is drawn. A bag contains red and green marbles. A marble is drawn from the bag and is not replaced. A second marble is then drawn from the bag. he solution is B: A bag contains red and green marbles. A marble is drawn from the bag and is not replaced. A second marble is then drawn from the bag. Since the first marble is not replaced, this impacts the probability of the second event. hus it is a dependent event. 8) Which situation describes INDEPENDEN events? A die is rolled, then it is rolled a second time. One card is chosen from a standard deck, it is set aside, then a second card is drawn. om chooses a Letter of the alphabet, then Beth must choose a different Letter from the alphabet. One student is chosen from Classroom A, then that student chooses one of his friends from Classroom A A die is rolled, then it is rolled a second time. he outcome of the first choice has no effect on the second choice. 9) In a lottery there are 9 balls, numbered to 9, in each of three bins. One ball will be selected from each bin. What are the odds of the numbers,, and being pulled IN HA ORDER7 to8 to0 to 80 to 78 ~xplanation: each event is independent. he chance of any number being pulled from the bin is.!: he odds for all three balls are.!: x!:. x!:. = , which means the odds are only to 78 of this happening. 79 0) If a die is rolled twice, what is the probability of rolling a and then a? 6 he solution is _..! he two events are independent since the outcome of one event does not impact the outcome of the other 6 event o find the probability, multiply the probabilities together. 6 - = usatestprep.com/modules/quiz _factory/key. php 8

5 9/0 USAestprep, Inc. ) A bag contains blue and yellow marbles. wo marbles are drawn without replacement. he probability of selecting a blue marble and then a yellow marble is 0.7, and the probability of selecting a blue marble on the first draw is 0.. ;lhat is the probability of selecting a yellow marble on the second draw, if the first marble drawn was blue? ~ 6 q %% 0% 67% o calculate probability of two dependent events you multiply their probabilities together. However, in this problem you were given the probability of both dependent events occurring and solving for one of the dependent events. he solution is found by solving for the second event: P(blue and yellow)= P(blue)"P(yellow) 0.7 = 0. P(yellow) P(yellow)= % = 67%. 0. ) Mary Katherine has a bag of red apples, yellow apples and green apples. Mary takes a red apple out of the bag and does not replace it. What is the probability that the next apple she takes out is yellow? he solution is _. Since Mary Katherine takes a red apple out of the bag, there are apples left. Five of those apples are yellow. So the probability of taking a yellow apple out of the bag is -. ) In Salem, 8% of the households have cable television and Internet access and 90% of the houses have cable television. What is the probability that a house has Internet access given that it has cable television? 8% 7% ~ ~% ~ ~ he solution is 9%. o solve this problem, we use the formula for conditional probability. P(lnternetiCable) = P(Cable and Internet). P(Cable) ) At Bay High School60% of all students have a car and an I pod and 70% of all students have a car. What is the probability that a student with a car also has an lpod? ~ 0% q ~ 68% 9% he solution is 86%. o solve this problem, we use the formula for conditional probability. P(lpodiCar) = P(Car and lpod). P(Car) es/ql.iz _factory/key.php /8

6 90 USAestprep, Inc. ) Do you go to the movies at Least twice a week? r ~~ ~Y~s r N~~~[ L Male ~.- i.li 80 I I ' j i Female j 6 7 /8 9 ;. ~,_~'----' \ otal i 0/7 j7sl Jamie wants to find out how many students at her school go to the movies at least twice a week. She interviews 7 students and records their gender and a yes if they go at least twice a week and no if they go Less than twice a week. She displays the results in the table. What is the probability that a male goes to the movies at Least twice a week (round to the thousandth)? ( he correct answer is 0.8. his is a conditional probability. Find the probability of someone going to the movies at least twice a week given they are male. P(go to movies given that they are male}=. 80 6) You are playing a game of Scrabble and have the SA tiles, E tiles, Z tile, M tiles, L tiles, and Y tile to choose from. What is the probability that you choose E or Yon your next draw? s o find the probability we use the mutually exclusive probability formula P( + P(. he probability of picking a E tile is.!: and the s probability of picking a Y tile is I.. he sum is.i.. 7) immy flipped a coin one hundred times. He got 6 heads and 8 tails. Which statement best describes this situation? % is the experimental probability of getting q 6% is the experimental probability of getting a head on a a head on a coin flip in this situation. coin flip in this situation. 6% is the theoretical probability of getting a head on a coin flip. he correct statement is 6% is the experimental probability of getting a head on a coin flip in this situation.. Experimental is what you get by doing the activity, theoretical probability if what you would expect to get, in this case % is the theoretical probability of getting a tail on a coin flip in this situation. ( http: llwww. usatestprep.com/modules/quiz _factory /key.php 68

7 90 USAestprep, Inc. 8) here are 0 marbles in a bag, and the marbles are either red or blue. Eric will randomly choose two marbles from the bag, without replacing the first one. If the probability of both marbles' being red is _, how many BLUE marbles are in the bag? Eric's probability on the first pick is _._ His probability of the second pick is x-l_ his will give a solution of x(x-l). }:_ is equal to and are the only consecutive numbers that when multiplied together equal. herefore there are red marbles in the bag 90 and 6 blue marbles. 9) here are marbles in a bag, and the marbles are either yellow or green. wo marbles will be randomly picked from the bag, without replacing the first one picked. he probability that both marbles will be yellow is.. How many GREEN marbles are in the bag? he probability of picking yellow first is -"-.he probability of picking yellow second is x-. his will give a solution of x (x- ),. is equivalent to lq_, and are the only two consecutive numbers that when multiplied together equal 0. herefore there are ~ellow and 7 green marbles in the bag. 0) You find a deck of cards and know that the deck has too many clubs and spades in it. he deck has 9 cards If you were to draw two cards without replacement, the probability of drawing a diamond and a club is spades are in the deck? 7 First set up a proportion of probability of diamond times-"- = : How many extra 7 -"- = 7. Solving for x tells you how many clubs are in the deck. Since x = 8 and there should only be clubs then you have extra clubs. With a total of 9 cards that means total you have 7 extra cards. If of them are clubs then the other must be spades. So the deck has extra spades. tww\n.usatestprep.com/modul es/qui z _factory/key.php 78

8 /9/0 USAestprep.!nc. ) here are cards, numbered through. If you pick a card, what is the probability that you choose an odd number or a two? 8 8 here are 8 odd cards and one card is a two. Since 8 + is 9, the probabitity is ~ or ~. ) A cookie jar contains 6 chocolate chip cookies, oatmeal cookies, 8 peanut butter cookies, and sugar cookies. If a cookie is pulled From the jar what is the probability that it is oatmeal or peanut butter? hese are mutually exclusive events so we use the formula P( + P(. he probability of picking an oatmeal cookie is..!. and the probability of picking a peanut butter cookie is"'} he sum of the probabilities is ~. ( trtl.p:/twww.usatestprep.com/modules/quiz _factory/key.php 8/8

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