Recommended problems from textbook

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1 Recommended problems from textbook Section 9-1 Two dice are rolled, one white and one gray. Find the probability of each of these events. 1. The total is The total is at least The total is less than The total is at most The total is The total is The total is between 3 and 7, inclusive. 8. The total is between, but does not include, 3 and The total is between 2 and 12, inclusive. 10. The total is The numbers are 2 and The gray die shows 2 and the white die shows The gray die shows 2 or the white die shows 5. Section 9-2 Q1. If you flip a coin, what is the probability that the result will be heads? Q2. If you flip the coin again, what is the probability that the second flip will be heads? Q3. Does the result of the second flip depend on the result of the first flip? Q4. What is 3 5 expressed as a percent? Q9. True or false: (ab) 2 = a 2 b 2 Q10. True or false: (a + b) 2 = a 2 + b 2 1. A card is drawn at random from a standard 52-card deck. 1

2 a. What term is used in probability for the act of drawing a card? b. How many outcomes are in the sample space? c. How many outcomes are in the event the card is a face card? d. Calculate P (the card is a face card). e. Calculate P (the card is black). f. Calculate P (the card is an ace). g. Calculate P (the card is between 3 and 7, inclusive). h. Calculate P (the card is the ace of clubs). i. Calculate P (the card belongs to the deck). j. Calculate P (the card is a joker). 2. A penny, a nickel, and a dime are flipped at the same time. Each coin can land either heads up (H) or tails up (T). a. What term is used in probability for the act of flipping the coins? b. One possible outcome is THT. List all eight outcomes in the sample space. c. How many outcomes are in the event exactly two of the coins show heads? d. Calculate P (HHT). e. Calculate P (exactly two heads). f. Calculate P (at least two heads). g. Calculate P (penny and nickel are tails). h. Calculate P (penny or nickel is tails). i. Calculate P (none are tails). j. Calculate P (zero, one, two, or three heads). k. Calculate P (four heads). Section 9-3 2

3 Q1. Simplify the fraction Q2. Evaluate: Q4. Multiply: ( 2 7 )( 3 4 ) Q5. Add: A salesperson has 7 customers in Denver and 13 customers in Reno. In how many different ways could she telephone a. A customer in Denver and then a customer in Reno b. A customer in Denver or a customer in Reno, but not both 2. A pizza establishment offers 12 vegetable toppings and 5 meat toppings. Find the number of different ways that you could select a. A meat topping or a vegetable topping b. A meat topping and a vegetable topping 3. A reading list consists of 11 novels and 5 biographies. Find the number of different ways a student could select a. A novel or a biography b. A novel and then a biography c. A biography and then another biography 4. A convoy of 20 cargo ships and 5 escort ships approaches the Suez Canal. In each scenario, in how many different ways could these vessels begin to go through the canal? a. A cargo ship and then an escort vessel b. A cargo ship or an escort vessel c. A cargo ship and then another cargo ship 5. The menu at Paesano s lists 7 salads, 11 entrees, and 9 desserts. How many different salad-entreedessert meals could you select? (Meals are considered to be different if any one thing is different.) 6. Admiral Motors manufactures cars with 5 different body styles, 11 different exterior colors, and 6 different interior colors. A dealership wants to display one of each possible variety of car in its showroom. Explain to the manager of the dealership why the plan would be impractical. 7. Consider the letters in the word LOGARITHM. a. In how many different ways could you select a vowel or a consonant? 3

4 b. In how many different ways could you select a vowel and then a consonant? c. How many different 3-letter words (for example, ORL, HLG, AOI) could you make using each letter no more than once in any one word? (There are three events: select the first letter, select the second letter, and select the third letter. Find the number of ways each event can occur, and then figure out what to do with the three results.) 8. Lee brought two jazz CDs and five rap CDs to play at the class picnic. a. In how many different ways could he choose a jazz CD and then a rap CD? b. In how many different ways could he choose a jazz CD or a rap CD? c. Lee s CD player allows him to load four CDs at once. The CDs will play in the order he loads them. How many different orderings of four CDs are possible? (See Problem 7 for a hint.) 9. There are 20 girls on the basketball team. Of these, 17 are over 16 years old, 12 are taller than 170 cm, and 9 are both older than 16 and taller than 170 cm. How many of the girls are older than 16 or taller than 170 cm? 10. Lyle s DVD collection includes 37 classic films and 29 comedies. Of these, 21 are classic comedies. How many DVDs does Lyle have that are classics or comedies? 11. The library has 463 books dealing with science and 592 books of fiction. Of these, 37 are science fiction books. How many books are either science or fiction? 12. The senior class has 367 girls and 425 students with brown hair. Of the girls, 296 have brown hair. In how many different ways could you select a girl or a brown-haired student from the senior class? 13. Seating Problem: There are ten students in a class and ten chairs, numbered 1 through 10. a. In how many different ways could a student be selected to occupy chair 1? b. After someone is seated in chair 1, how many different ways are there of seating someone in chair 2? c. In how many different ways could chairs 1 and 2 be filled? d. If two of the students are sitting in chairs 1 and 2, in how many different ways could chair 3 be filled? e. In how many different ways could chairs 1, 2, and 3 be filled? f. In how many different ways could all ten chairs be filled? Do you find this surprising? 14. Baseball Team Problem: Nine people on a baseball team are trying to decide who will play each position. a. In how many different ways could they select a person to be pitcher? b. After someone has been selected as pitcher, in how many different ways could they select someone to be catcher? 4

5 c. In how many different ways could they select a pitcher and a catcher? d. After the pitcher and catcher have been selected, in how many different ways could they select a first-base player? e. In how many different ways could they select a pitcher, catcher, and first-base player? f. In how many different ways could all nine positions be filled? Do you find this surprising? Section 9-4 Q1. If the outcomes of a random experiment are equally likely, then the probability of an event is defined to be...? Q2. For events A and B, n(a and then B) =...? Q3. If events A and B are mutually exclusive, then n(a or B) =...? Q4. If events A and B are not mutually exclusive, then n(a or B) =...? 1. The Hawaiian alphabet has 12 letters. How many permutations could be made using a. Two different letters b. Four different letters c. Twelve different letters 2. Fran Tick takes a ten-problem precalculus test. The problems may be worked in any order. a. In how many different orders could she work all ten of the problems? b. In how many different orders could she work any seven of the ten problems? 3. Triangles are often labeled by placing a different letter at each vertex. In how many different ways could a given triangle be labeled using any of the 26 letters of the alphabet? 4. Tom, Dick, and Harry each draw two cards from a standard 52-card deck and place them face up in a row. The cards are not replaced. Tom goes first. Find the number of different orders in which a. Tom could draw his two cards b. Dick could draw his two cards after Tom has already drawn c. Harry could draw his two cards after Tom and Dick have drawn theirs 5. Frost Bank has seven vice presidents, but only three spaces in the parking lot are labeled Vice President. In how many different ways could these spaces be occupied by the vice presidents cars? 6. A professor says to her class, You may work these six problems in any order you choose. There are 100 students in the class. Is it possible for each student to work the problems in a different order? Explain. 5

6 Section 9-5 Q1. 4! =...? Q2. 4! 4 =...? Q3. 3! 3 =...? Q4. 2! 2 =...? Q5. 1! 1 =...? Q7. Write 5 P 5 as a factorial. Q8. Write n P n as a factorial. Q9. Express as a percent rounded to the nearest integer. 13. Twelve people apply to go on a biology field trip, but there is room in the car for only five of them. In how many different ways could the group of five making the trip be chosen? How can you tell that a number of combinations is being asked for, not a number of permutations? 14. Seven people come to an evening bridge party. Only four people can play the game at any one time, so they decide to play as many games as it takes to use every possible foursome once. How many games would have to be played? Could all of these games be played in one evening? 15. A donut franchise sells 34 varieties of donuts. Suppose one of the stores decides to make sample boxes with six different donuts in each box. How many different sample boxes could be made? Would it be practical to stock one of each kind of box? 16. Just before each Supreme Court session, each of the nine justices shakes hands with every other justice. How many handshakes take place? 17. Horace Holmsley bought blueberries, strawberries, watermelon, grapes, plums, and peaches. Find the number of different fruit salads he could make if he uses a. Three ingredients b. Four ingredients c. Three ingredients or four ingredients d. All six ingredients 18. A pizzeria offers 11 different toppings. Find the number of different kinds of pizza it could make using a. Three toppings b. Five toppings 6

7 c. Three toppings or five toppings d. All 11 toppings 19. A standard deck of playing cards has 52 cards. a. How many different five-card poker hands could be formed from a standard deck? b. How many different 13-card bridge hands could be formed? c. How can you tell that numbers of combinations are being asked for, not numbers of permutations? Section 9-6 Q1. If A and B are mutually exclusive, then n(a or B) =...? Q2. If A and B are not mutually exclusive, then n(a or B) =...? Q3. n(a and B) = n(a) n(b A), where n(b A) is the number of ways B can happen...? Q4. The number of combinations of five objects taken three at a time is equal to...? Q5. The number of permutations of five objects taken three at a time is equal to...? Q6. Why is a number of permutations greater than the corresponding number of combinations? 7

ATHS FC Math Department Al Ain Remedial worksheet. Lesson 10.4 (Ellipses)

ATHS FC Math Department Al Ain Remedial worksheet Section Name ID Date Lesson Marks Lesson 10.4 (Ellipses) 10.4, 10.5, 0.4, 0.5 and 0.6 Intervention Plan Page 1 of 19 Gr 12 core c 2 = a 2 b 2 Question