Practice Quiz - Permutations & Combinations

Transcription

1 Algebra 2 Practice Quiz - Permutations & Combinations Name Date Period Determine whether the scenario involves independent or dependent events. Then find the probability. 1) A box of chocolates contains six milk chocolates and five dark chocolates. You randomly pick a chocolate and eat it. Then you randomly pick another piece. The first piece is milk chocolate and the second piece is dark chocolate. Independent; D) Dependent; E) Independent; 2) There are six nickels and five dimes in your pocket. You randomly pick a coin out of your pocket and place it on a counter. Then you randomly pick another coin. Both coins are nickels. Independent; B) None of these Dependent; D) Independent; E) Independent; Find the probability of each event. 3) A car dealership has nine cars in the lot. Unfortunately, the keys to the cars have been mixed up. The manager randomly grabs a key and tries to start a car. A salesman also randomly picks a different key and tries to start another car. What is the probability that both cars start? % B) % % D) % 4) A technician is launching fireworks near the end of a show. Of the remaining nine fireworks, five are blue and four are red. If she launches five of them in a random order, what is the probability that all of them are blue? % B) % % D) % -1-

2 List all possible combinations. 5) T, V, W, X, taken two at a time TV TW TX B) TV TW TX VW VX WX VT VW VX WT WV WX XT XV XW List all possible permutations. 6) 4, 5, 6, 7, taken two at a time B) State if each scenario involves a permutation or a combination. Then find the number of possibilities. 7) There are 140 people at a meeting. They each shake hands with everyone else. How many handshakes were there? 8) A group of 20 people are going to run a race. The top three runners earn gold, silver, and bronze medals. d f2t0b1x6d pkgurtzah PSaoUfbtxwLa_rEeV nlelsc\.n Q zaslilq brgixgrhutasg YrIews_eorpvveed].G \ kmoa[djez AwUiatfhb ei\npfnisnuiqtjev razlbgaefbkrda^ S2H. -2-

3 Algebra 2 Practice Quiz - Permutations & Combinations Name Date Period Determine whether the scenario involves independent or dependent events. Then find the probability. 1) A box of chocolates contains six milk chocolates and five dark chocolates. You randomly pick a chocolate and eat it. Then you randomly pick another piece. The first piece is milk chocolate and the second piece is dark chocolate. Independent; *D) Dependent; E) Independent; 2) There are six nickels and five dimes in your pocket. You randomly pick a coin out of your pocket and place it on a counter. Then you randomly pick another coin. Both coins are nickels. Independent; B) None of these * Dependent; D) Independent; E) Independent; Find the probability of each event. 3) A car dealership has nine cars in the lot. Unfortunately, the keys to the cars have been mixed up. The manager randomly grabs a key and tries to start a car. A salesman also randomly picks a different key and tries to start another car. What is the probability that both cars start? % *B) % % D) % 4) A technician is launching fireworks near the end of a show. Of the remaining nine fireworks, five are blue and four are red. If she launches five of them in a random order, what is the probability that all of them are blue? % B) % % D) % * -1-

4 List all possible combinations. 5) T, V, W, X, taken two at a time * TV TW TX B) TV TW TX VW VX WX VT VW VX WT WV WX XT XV XW List all possible permutations. 6) 4, 5, 6, 7, taken two at a time *B) State if each scenario involves a permutation or a combination. Then find the number of possibilities. 7) There are 140 people at a meeting. They each shake hands with everyone else. How many handshakes were there? Combination; 9,730 8) A group of 20 people are going to run a race. The top three runners earn gold, silver, and bronze medals. Permutation; 6,840-2-

5 Algebra 2 Practice Quiz - Permutations & Combinations Name Date Period Determine whether the scenario involves independent or dependent events. Then find the probability. 1) You flip a coin twice. The first flip lands tails-up and the second flip lands heads-up. None of these Independent; D) Independent; E) Dependent; 2) A bag contains four red marbles and seven blue marbles. You randomly pick a marble and then return it to the bag before picking another marble. The first marble is red and the second marble is blue. Independent; B) Independent; Dependent; D) Dependent; Find the probability of each event. 3) Stefan is carrying ten pages of math homework and two pages of English homework. A gust of wind blows the pages out of his hands and he is only able to recover ten random pages. What is the probability that he recovers all of his math homework? % B) % % D) % 4) A technician is launching fireworks near the end of a show. Of the remaining twelve fireworks, seven are blue and five are red. If she launches seven of them in a random order, what is the probability that all of them are blue? % B) None of these % D) % E) % -1-

6 List all possible combinations. 5),,,, taken two at a time None of these B) List all possible permutations. 6),,,, taken two at a time B) State if each scenario involves a permutation or a combination. Then find the number of possibilities. 7) The batting order for seven players on a 11 person team. 8) You are setting the combination on a five-digit lock. You want to use the numbers but don't care what order they are in. -2-

7 Algebra 2 Practice Quiz - Permutations & Combinations Name Date Period Determine whether the scenario involves independent or dependent events. Then find the probability. 1) You flip a coin twice. The first flip lands tails-up and the second flip lands heads-up. None of these Independent; *D) Independent; E) Dependent; 2) A bag contains four red marbles and seven blue marbles. You randomly pick a marble and then return it to the bag before picking another marble. The first marble is red and the second marble is blue. * Independent; B) Independent; Dependent; D) Dependent; Find the probability of each event. 3) Stefan is carrying ten pages of math homework and two pages of English homework. A gust of wind blows the pages out of his hands and he is only able to recover ten random pages. What is the probability that he recovers all of his math homework? * % B) % % D) % 4) A technician is launching fireworks near the end of a show. Of the remaining twelve fireworks, seven are blue and five are red. If she launches seven of them in a random order, what is the probability that all of them are blue? % B) None of these % * D) % E) % -1-

8 List all possible combinations. 5),,,, taken two at a time None of these *B) List all possible permutations. 6),,,, taken two at a time * B) State if each scenario involves a permutation or a combination. Then find the number of possibilities. 7) The batting order for seven players on a 11 person team. Permutation; 1,663,200 8) You are setting the combination on a five-digit lock. You want to use the numbers but don't care what order they are in. Permutation;

9 Algebra 2 Practice Quiz - Permutations & Combinations Name Date Period Determine whether the scenario involves independent or dependent events. Then find the probability. 1) A box of chocolates contains four milk chocolates and eight dark chocolates. You randomly pick a chocolate and eat it. Then you randomly pick another piece. The first piece is milk chocolate and the second piece is dark chocolate. Dependent; D) Dependent; E) Dependent; 2) A cooler contains fifteen bottles of sports drink: seven lemon-lime flavored and eight orange flavored. You randomly grab a bottle and give it to your friend. Then, you randomly grab a bottle for yourself. You and your friend both get lemon-lime. Dependent; D) Independent; E) Dependent; Find the probability of each event. 3) A gambler places a bet on a horse race. To win, he must pick the top three finishers in any order. Ten horses of equal ability are entered in the race. Assuming the horses finish in a random order, what is the probability that the gambler will win his bet? % % E) % B) None of these D) % 4) Ming is carrying nine pages of math homework and two pages of English homework. A gust of wind blows the pages out of her hands and she is only able to recover nine random pages. What is the probability that she recovers all of her math homework? % B) % % E) % D) None of these -1-

10 List all possible combinations. 5) 4, 5, 6, 7, taken two at a time B) List all possible permutations. 6) 4, 5, 6, 7, taken two at a time 45 B) None of these 45 State if each scenario involves a permutation or a combination. Then find the number of possibilities. 7) There are 40 applicants for four jobs: Computer Programmer, Software Tester, Manager, and Systems Engineer. 8) You are setting the combination on a three-digit lock. You want to use the numbers 624 but don't care what order they are in. -2-

11 Algebra 2 Practice Quiz - Permutations & Combinations Name Date Period Determine whether the scenario involves independent or dependent events. Then find the probability. 1) A box of chocolates contains four milk chocolates and eight dark chocolates. You randomly pick a chocolate and eat it. Then you randomly pick another piece. The first piece is milk chocolate and the second piece is dark chocolate. Dependent; D) Dependent; *E) Dependent; 2) A cooler contains fifteen bottles of sports drink: seven lemon-lime flavored and eight orange flavored. You randomly grab a bottle and give it to your friend. Then, you randomly grab a bottle for yourself. You and your friend both get lemon-lime. Dependent; * D) Independent; E) Dependent; Find the probability of each event. 3) A gambler places a bet on a horse race. To win, he must pick the top three finishers in any order. Ten horses of equal ability are entered in the race. Assuming the horses finish in a random order, what is the probability that the gambler will win his bet? % % E) % * B) None of these D) % 4) Ming is carrying nine pages of math homework and two pages of English homework. A gust of wind blows the pages out of her hands and she is only able to recover nine random pages. What is the probability that she recovers all of her math homework? * % B) % % E) % D) None of these -1-

12 List all possible combinations. 5) 4, 5, 6, 7, taken two at a time B) * List all possible permutations. 6) 4, 5, 6, 7, taken two at a time 45 *B) None of these 45 State if each scenario involves a permutation or a combination. Then find the number of possibilities. 7) There are 40 applicants for four jobs: Computer Programmer, Software Tester, Manager, and Systems Engineer. Permutation; 2,193,360 8) You are setting the combination on a three-digit lock. You want to use the numbers 624 but don't care what order they are in. Permutation; 6-2-