Date Period State if each scenario involves a permutation or a combination. Then find the number of possibilities. ncr or npr

Transcription

1 Algebra 2 G h2y0cic pk_ultta` LSeoxfftrwFaPrXeq qlolkco.p E nalltls jroifgvhztdso mrxeosbe^ravyeddt. Ultimate Probability Name Date Period State if each scenario involves a permutation or a combination. Then find the number of possibilities. ncr or npr ) There are 40 applicants for four Software Tester positions. 2) A team of 8 lacrosse players needs to choose a captain and co-captain. 3) A group of people are going to run a race. The top finishers advance to the finals. 4) A group of people are going to run a race. The top three runners earn gold, silver, and bronze medals. Find the number of possible outcomes in the sample space. n m or n! 5) Ten rooms in a house need to be painted. Each room can be painted white or yellow. 6) Seven books need to be placed on a shelf. You randomly arrange the books on the shelf from left to right. ) Four rooms in a house need to be painted. Each room can be painted white, yellow, or pink. 8) A padlock's combination is six digits long. Determine whether the scenario involves independent or dependent events. ONLY IF it is independent, then find the probability. If it is dependent, mark it that way and you are done. 9) You flip a coin twice. The first flip lands tails-up and the second flip also lands tails-up. 0) You flip a coin and then roll a fair six-sided die. The coin lands heads-up and the die shows a five. G O2J0XFs JKruWtCah hstorfltswjamr^ex sljljcc.r I RADlvlF xrjibgah[tfsc brzeqsaewruv[esdf.a l NMuamd]eO LwviztShF JIZnQflitnpi[t[eW EA\lUgxeGbhr`aX L2R. --

2 ) A bag contains three red marbles and six marble and then pick a second marble without returning the marbles to the bag. Both marbles are red. 2) A bag contains six red marbles and four marble and then return it to the bag before picking another marble. The first marble is red and the second marble is blue. 3) A bag contains four red marbles and eight marble and then return it to the bag before picking another marble. The first marble is red and the second marble is blue. 4) A cooler contains ten bottles of sports drink: four lemon-lime flavored and six orange flavored. You randomly grab a bottle and give it to your friend. Then, you randomly grab a bottle for yourself. Your friend gets a lemon-lime and you get an orange. Events A and B are independent. Find the missing probability. ("AND" signals to us to multiply) 5) P(A) = 2 5 P(B) = 6) P(A) = 5 P(B) = 5 ) P(A) = P(B) = 4 8) P(A) = 3 4 P(B) = 2 5 Determine if the scenario involves mutually exclusive events. 9) There are four nickels and five dimes in your pocket. One of the nickels and two from your pocket. It is a dime or is Canadian currency. ) A cooler contains ten sports drinks: six lemon-lime and four orange. Five of the lemon-lime and three of the orange drinks are cold. The others are still warm. You randomly grab a bottle. It is orange flavored or cold. K f2h0nok WKiufttar ESQoyfjtpwFaurYeS nltluce.i n _AXlflu urjiegbhwtvsk erne[sienravzerd`.p w ]MwacdfeL ywdictjhi fianbfgijnaiktbee qaplgg`eebbrpad ]2N. -2-

3 2) A box contains four red playing cards numbered one to four. The box also pick a playing card. It is black or has an odd number. 22) There are twelve shirts in your closet, six blue and six green. One of the blue shirts and three of the green shirts fit well. The others are too big. You randomly select a shirt to wear. It is blue or is too big. 23) A magazine contains fourteen pages. You open to a random page. The page number is eleven or thirteen. 24) There are thirteen shirts in your closet, four blue, five green, and four red. You randomly select one to wear. It is blue or green. Determine if the scenario involves mutually exclusive events. Then find the probability. ("OR" signals to us to add) 25) A litter of kittens consists of two gray kittens, two black kittens, and two mixed-color kittens. You randomly pick one kitten. The kitten is gray or mixed-color. 26) You roll a fair six-sided die. The die shows a four or a six 2) A litter of kittens consists of three gray kittens, two black kittens, and two mixed-color kittens. You randomly pick one kitten. The kitten is gray or mixed-color. 28) You roll a fair six-sided die. The die shows a two or a six 29) A bag contains three red marbles, four blue marbles, and five yellow marbles. You randomly pick a marble. The marble is red or blue. 30) A basket contains four apples, five peaches, and five pears. You randomly select a piece of fruit. It is an apple or a peach. d p2w0nek ek_uxtxau HSNoyf]t[woaArCeZ DLDLcCS.o H IAblFli SrCiZgRh[tpsl krbersvetrdvfeldw.m a NMvaPdoeM vwyidtrhw HIunKfGilnYiQtheU waalzghetbdraaw W2w. -3-

4 3) P(A) = P(B) = ) P(A) = 4 P(B) = 33) P(A) = 2 5 P(B) = 34) P(A) = P(B) = These examples are NOT mutually exclusive. In these examples you must ADD the probabilities but be sure to subtract any repeated items in the crossover. m n + m 2 n - crossover/n 35) A box contains six red playing cards numbered one to six. The box also pick a playing card. It is red or has an even number. 36) A jar contains three orange marbles numbered one to three. The jar also contains five green marbles numbered one to five. You randomly pick a marble. It is green or has a number greater than two. 3) A box contains five red playing cards numbered one to five. The box also pick a playing card. It is black or has a number less than three. 38) A jar contains five orange marbles numbered one to five. The jar also contains six green marbles numbered one to six. You randomly pick a marble. It is green or has a number greater than three. 39) There are four nickels and four dimes in your pocket. One of the nickels and one from your pocket. It is a dime or is US currency. 40) There are five nickels and five dimes in your pocket. Three of the nickels and four from your pocket. It is a dime or is Canadian currency. V i2y0kso CKDuitaaJ PSKoEfVtbwoa\rgeY WLkLTCv.O y za\lslb BrPi\gmhQt`s^ Sr_ejsYegrNvYeDdh.F Y hmsandjee EwAiJtihJ JI\nPfWiFn^iwtPen AAnlBgrejbXr\ac [2f. -4-

5 Algebra 2 E F2B0fba ukwuyt\af tszoyfttdwxaerbe` nlvl_ct.i I YAMlKlt lrciogshetzsn srse[stekr[v\eadv. Ultimate Probability Name Date Period State if each scenario involves a permutation or a combination. Then find the number of possibilities. ncr or npr ) There are 40 applicants for four Software Tester positions. Combination; 9,390 2) A team of 8 lacrosse players needs to choose a captain and co-captain. Permutation; 306 3) A group of people are going to run a race. The top finishers advance to the finals. Combination; 6,960 4) A group of people are going to run a race. The top three runners earn gold, silver, and bronze medals. Permutation; 6,840 Find the number of possible outcomes in the sample space. n m or n! 5) Ten rooms in a house need to be painted. Each room can be painted white or yellow ) Seven books need to be placed on a shelf. You randomly arrange the books on the shelf from left to right ) Four rooms in a house need to be painted. Each room can be painted white, yellow, or pink. 8) A padlock's combination is six digits long Determine whether the scenario involves independent or dependent events. ONLY IF it is independent, then find the probability. If it is dependent, mark it that way and you are done. 9) You flip a coin twice. The first flip lands tails-up and the second flip also lands tails-up. 0) You flip a coin and then roll a fair six-sided die. The coin lands heads-up and the die shows a five. Independent; 4 = 0.25 Independent; 2» A P2U0ILV wkcudteal ssmoefltvwzasreen TLZLbCM.N i RAZltlp IrwiSgOh_tvsW ireezsgeprxvmefdc.z k TMpaxd]eo uwairtbhs HImncfziQnniMt^ee LAPlngzeDbLrgaq p2n. --

6 ) A bag contains three red marbles and six marble and then pick a second marble without returning the marbles to the bag. Both marbles are red. 2) A bag contains six red marbles and four marble and then return it to the bag before picking another marble. The first marble is red and the second marble is blue. Dependent Independent; 6 25 = ) A bag contains four red marbles and eight marble and then return it to the bag before picking another marble. The first marble is red and the second marble is blue. Independent; 2 9» ) A cooler contains ten bottles of sports drink: four lemon-lime flavored and six orange flavored. You randomly grab a bottle and give it to your friend. Then, you randomly grab a bottle for yourself. Your friend gets a lemon-lime and you get an orange. Dependent Events A and B are independent. Find the missing probability. ("AND" signals to us to multiply) 5) P(A) = 2 5 P(B) = 6) P(A) = 5 P(B) = ) P(A) = P(B) = 4 8) P(A) = 3 4 P(B) = Determine if the scenario involves mutually exclusive events. 9) There are four nickels and five dimes in your pocket. One of the nickels and two from your pocket. It is a dime or is Canadian currency. Not mutually exclusive ) A cooler contains ten sports drinks: six lemon-lime and four orange. Five of the lemon-lime and three of the orange drinks are cold. The others are still warm. You randomly grab a bottle. It is orange flavored or cold. Not mutually exclusive s b2l0iuz ukhurtwag CSSo`fJtcwoaMr]ej AL\L[C[.U R yaplcll _rwieglhotbsv Qrpe`sceLr_vJeZdP.[ ` amiagdzev pwdiutihv qiqnefyiqnoistjea yaelsgieab]raab G2[. -2-

7 2) A box contains four red playing cards numbered one to four. The box also pick a playing card. It is black or has an odd number. Not mutually exclusive 22) There are twelve shirts in your closet, six blue and six green. One of the blue shirts and three of the green shirts fit well. The others are too big. You randomly select a shirt to wear. It is blue or is too big. Not mutually exclusive 23) A magazine contains fourteen pages. You open to a random page. The page number is eleven or thirteen. Mutually exclusive 24) There are thirteen shirts in your closet, four blue, five green, and four red. You randomly select one to wear. It is blue or green. Mutually exclusive Determine if the scenario involves mutually exclusive events. Then find the probability. ("OR" signals to us to add) 25) A litter of kittens consists of two gray kittens, two black kittens, and two mixed-color kittens. You randomly pick one kitten. The kitten is gray or mixed-color. 26) You roll a fair six-sided die. The die shows a four or a six 3» » ) A litter of kittens consists of three gray kittens, two black kittens, and two mixed-color kittens. You randomly pick one kitten. The kitten is gray or mixed-color. 28) You roll a fair six-sided die. The die shows a two or a six 3» » ) A bag contains three red marbles, four blue marbles, and five yellow marbles. You randomly pick a marble. The marble is red or blue. 30) A basket contains four apples, five peaches, and five pears. You randomly select a piece of fruit. It is an apple or a peach. 2» » q H2n0BGT GKmupt\aJ KSCoXfktGwjaHrOer llvlic\.h p qaqldlm UroiugXhvthsA RraeZsEeYryvUeQdO.i d mmkamdoeh ywjiqtrhf yienlfgidnxiytgeg QAhlAgoegb^rzaZ u2y. -3-

8 3) P(A) = P(B) = ) P(A) = 4 P(B) = ) P(A) = 2 5 P(B) = 34) P(A) = P(B) = These examples are NOT mutually exclusive. In these examples you must ADD the probabilities but be sure to subtract any repeated items in the crossover. m n + m 2 n - crossover/n 35) A box contains six red playing cards numbered one to six. The box also pick a playing card. It is red or has an even number. 9» ) A jar contains three orange marbles numbered one to three. The jar also contains five green marbles numbered one to five. You randomly pick a marble. It is green or has a number greater than two. 3 4 = 0.5 3) A box contains five red playing cards numbered one to five. The box also pick a playing card. It is black or has a number less than three. 5 8 = ) A jar contains five orange marbles numbered one to five. The jar also contains six green marbles numbered one to six. You randomly pick a marble. It is green or has a number greater than three. 8» ) There are four nickels and four dimes in your pocket. One of the nickels and one from your pocket. It is a dime or is US currency. 40) There are five nickels and five dimes in your pocket. Three of the nickels and four from your pocket. It is a dime or is Canadian currency. 8 = = 0.8 ` p2x0nyn `Kfu[tzaR ASpomfTtWwOaZrQee XLALECf.E X MASlqln ernikgjh\t_s` arlegsnefrhvzeddn.z x mm`azddet pwjirtehs dixntffidnxigtjet OAMlPgBeWbzrOaY X2R. -4-