1. A factory manufactures plastic bottles of 4 different sizes, 3 different colors, and 2 different shapes. How many different bottles are possible?


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1 Unit 8 Quiz Review Short Answer 1. A factory manufactures plastic bottles of 4 different sizes, 3 different colors, and 2 different shapes. How many different bottles are possible? 2. A pizza corner offers a choice of 2 types of pizza bases and 8 types of pizza toppings. How many different single topping pizzas can a customer order? 3. Joe wants to buy a pair of shoes. His shoe size is available in 4 designs and 5 colors in a particular shop. From how many combinations of designs and colors can he choose? 4. In a high school, a student has an option of 3 foreign languages, training for 4 different musical instruments, and 6 types of outdoor activities. How many ways a student can select a foreign language, an instrumental training, and an outdoor activity? 5. There are 16 girls and 20 boys in a class. A team of 2 students is to be selected for preparing a science project from this class. How many ways a pair of a boy and a girl can be selected from this class? 6. John is getting his ATM card activated. He must select a password containing 4 nonzero digits to be able to use the card. How many passwords are allowed if no digit may be used more than once?
2 7. Tina has to create a password for the security of a software program file. She wants to use a password with 3 letters. How many passwords are allowed if no letters are repeated and the password is not case sensitive? 8. There are 9 children playing in a playground. In a game, they all have to stand in a line such that the youngest child is at the beginning of the line. How many ways can the children be arranged in the line? 9. For a college debate competition, Daniel must select one topic of six topics to speak at the first level. He must also select a different topic from the same list to speak at the second level of the competition. How many ways can he choose the topics for the two levels? There are 24 children in a class, 16 brownhaired and 8 blackhaired. Two students are randomly selected for a stage performance. Find the probability of the following selection. 10. P(2 brownhaired children) 11. P(2 blackhaired children) 12. P(1 brownhaired and 1 blackhaired child) Laura has moved to a new apartment. Her schoolbooks comprising of different subjects are mixed in a bag during the move. Four books are of mathematics, three are English, and six are science. If Laura opens the bag and selects books at random, find the given probability. 13. P(3 mathematics books)
3 14. P(3 English books) 15. P(1 science and 2 mathematics books) 16. P(1 book of each subject) 17. P(2 mathematics and 1 history book) 18. A fruit basket contains 6 apples and 8 oranges. Sarah randomly selects one, puts it back, and then randomly selects another. What is the probability that both selections were oranges? 19. On a bookshelf, there are 5 fiction and 4 nonfiction books. Paul randomly selects one, puts it back, and then randomly selects another. What is the probability that both selections were fiction books? 20. In a basket, there are 7 male kittens and 5 female kittens. Donna randomly selects one, puts it back, and then randomly selects another. What is the probability that both selections were female kittens?
4 21. A box contains 6 nuts, 8 bolts, and 4 screws. If 3 objects are selected in succession randomly, what is the probability of selecting a nut, then a bolt, then a screw, if replacement occurs each time? 22. A bag contains 6 red, 7 blue, and 5 green coins. If 3 coins are randomly selected in succession, what is the probability of selecting a red coin, then a blue coin, and then a green coin, if replacement occurs each time? 23. A jar contains 3 chocolate cookies, 5 peanut butter cookies, and 6 coconut cookies. If 3 cookies are selected in succession, what is the probability of selecting chocolate, then peanut butter, and then coconut cookies, if replacement occurs each time? 24. What is the probability of getting a 6 each time if a dice is rolled 4 times? 25. What is the probability of drawing a spade each time a card is drawn from a deck of 52 cards 3 times, if replacement occurs each time? 26. What is the probability of getting tails each time if a coin is tossed 4 times? 27. What is the probability of getting a 4 each time if a die is rolled 3 times?
5 Determine whether the given event is mutually exclusive or inclusive. Then find the probability. 28. A card is drawn from a standard deck of cards. P(queen or jack) 29. A coin is tossed. P(head or tail) 30. From a bag containing 5 white balls, 5 black balls, and 5 red balls, one ball is drawn. P(white or black) 31. A card is drawn from a standard deck of cards. P(6 or ace) A dice is rolled. What is the probability of rolling the following? 32. an even number or an odd number 33. a multiple of 2 or a multiple of a multiple of 3 or a multiple of 4
6 35. Each of the numbers from 1 to 50 is written on a tile and the tiles are placed upside down on the top of a table. If a tile is picked up at random, what is the probability that the number on the tile is a multiple of 7 or a multiple of 8? 36. A bag contains 12 pencils, 6 ball pens, and 2 sketch pens. Ronald takes out one writing object from this bag to note down some important information. What is the probability that a ball pen or a pencil is selected? Determine whether the given event is independent or dependent. Then find the probability. 37. There are 3 peanut butter and 4 vegetable sandwiches in a tray. Dennis chooses 3 of them at random. What is the probability that he chooses 2 vegetable sandwiches one after the other, and then 1 peanut butter sandwich? 38. A bag contains 4 black, 5 red, and 6 pink balls. If 3 balls are selected one after the other without replacement, what is the probability that 3 red balls are chosen? 39. There are 3 literature books, 4 geography books, and 3 science books on a shelf. If 3 books are chosen at random one after the other, what is the probability that a literature book, a geography book, and a science book are selected if replacement does not take place? 40. A bowl contains 3 red, 8 blue, and 7 black beads. Margaret randomly selects 3 beads. Find the probability that one bead of each color is selected one after the other without replacement.
7 41. When Charles randomly chooses a fruit from a basket of apples and oranges, the odds are 5 to 3 that he will select an orange. What is the probability that he chooses 2 oranges, if fruits are not replaced? 42. There are 3 strawberry ice creams, 4 chocolate ice creams, and 7 vanilla ice creams on a tray. Barbara selects 2 ice creams at random without replacement. What is the probability that she selects 2 chocolate ice creams? 43. There are 6 glasses of natural fruit juices, 7 glasses of soft drinks, and 4 glasses of milk shakes served at a gettogether. Savio chooses 2 glasses in succession without replacement. Find the probability that he selects a glass of natural fruit juice and a milk shake. Solve each permutation or combination P P P P C C C C C 6 9 C P 44 C 2
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