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PROBABILITY: throwing with one die 1. P(throwing a 4) 2. P(throwing a 1 or 6) 3. P(throwing 2 or greater) 4. P(throwing a maximum of 3) 5. P(throwing a number greater than 4) 6. P(throwing a number less than 5) 7. P(throwing a minimum of 2) 8. P(throwing at least 4) 9. P(throwing a number more than 5) 10. P(throwing a number between 1 and 6) 11. P(throwing a 1, 2, 3, 4, 5 or 6) 12. P(throwing a 7) 13. P(throwing an even number) 14. P(throwing an odd number) 15. P(throwing a prime number) 16. P(throwing a square number) 17. P(throwing a cube number) 18. P(throwing a number exactly divisible by 3) 19. P(throwing a number exactly divisible by 2 and 3) 20. P(throwing a number smaller than 2 or greater than 4) 21. P(throwing a number smaller than 3 and greater than 5) 22. P(throwing a number which is not 6) PROBABILITY: picking one card from a pack of playing cards 1. P(picking the ace of hearts) 2. P(picking a 7) 3. P(picking a black card) 4. P(picking a black 8) 5. P(picking a picture card) 6. P(picking a card of the suit of spades) 7. P(picking a card which is not an ace) 8. P(picking a picture card of clubs) 9. P(picking a 2 or a 5) 10. P(picking a 4 and a 9) 11. P(picking a card of the suit of clubs, spades or hearts) 12. P(picking a card which is not a picture card) 13. P(picking a 10 or a red card) 14. P(picking a red 10) 15. P(picking a red Jack or a card of the suit of diamonds) 16. P(picking a red picture card) 17. P(picking a card which is of the suit of diamonds and not a picture card) 18. P(picking a black picture card or a card of the suit of clubs) 19. P(picking a card which is not a Queen) 20. P(picking a card which is not red and not a 3) 21. P(picking a picture card which is not of the suit of hearts) 22. P(picking a card of the suit of hearts which is not a picture card) PROBABILITY: picking at random one item from a box 1. 5 black marbles 3 white marbles 1 marble 2. 8 green crayons 4 red crayons 6 blue crayons a. P(picking a black marble) b. P(picking a white marble) c. P(picking a blue marble) a. P(picking a red crayon) b. P(picking a crayon which is not red) c. P(picking a blue or red crayon) a. P(not picking a bag of crisps) b. P(picking chocolate or crisps) c. P(picking chocolate and crisps) a. P(winning the first prize) b. P(winning a prize) c. P(not winning a prize) a. P(picking a study book ) b. P(picking an English book) c. P(picking a French book or a study book) a. P(picking a red ball with a two on it) b. P(picking a ball with a one on it) c. P(picking a ball which is not green) 1 crayon 3. 12 bars of chocolate 3 bags of crisps 9 packets of chewing gum 1 item 4. 1 ticket with the first prize 3 tickets with a second prize 6 tickets with a third prize 90 tickets without a prize 1 ticket 5. 6. 12 English study books 8 French study books 6 English cook books 14 French cook books red blue 1 book green 1 ball PROBABILITY: spinning a spinner once a. P(spinning a 4) b. P(not spinning a 4) c. P(spinning an even number) d. P(spinning a prime number) a. P(spinning a square number) b. P(not spinning a square number) c. P(spinning a number which is divisible by 2 and 3 ) 6 d. P(spinning a number which is divisible by 2 or 3 ) 1 a. P(spinning a cube number) b. P(not spinning a cube number) c. P(spinning a multiple of 4) d. P(spinning at least a 6) a. P(spinning a one) b. P(not spinning a one) c. P(spinning an odd number) d. P(spinning a triangular number) a. P(spinning a 4) b. P(spinning a 1) c. P(spinning a 2) d. P(spinning a 5) e. P(not spinning a 5) 1. 4 6 8 2. 4 9 9 3. 4 4 1 1 8 4. 4 2 1 3 5 6 5. 1 2 5 80° 40° 4 60° 3 PROBABILITY: miscellaneous questions with single events 1. One letter is chosen at random from the letters in the word SALE. What is the probability that it is A ? 2. What is the probability that a red pencil is chosen from a box containing 10 different coloured pencils? 3. What is the probability of choosing a square number from the fifty numbers 1 till 50 ? 4. What is the probability of choosing an integer that is exactly divisible by 4 from the list 6, 7, 8, 9, 10, 11, 12 ? 5. Two hundred tickets are sold in a raffle with one 1st prize, three 2nd prizes and five 3rd prizes. If you bought 1 ticket, what is the probability that a. you will win a third prize? b. you will win a prize? 6. One card is chosen at random from a pack of 52 playing cards. What is the probability that it is a. a card between 5 and 9 ? b. a black picture card or a King? 7. 8. A whole number is chosen from the first 15 positive whole numbers. What is the probability that it is divisible by 3 or by 4 ? There are 16 girls in a class of 24. A student is chosen at random. What is the probability that the chosen student is a. a girl? b. a boy? 9. A box contains 12 chocolates with soft centres and 18 chocolates with hard centres. Ellen chooses a chocolate at random from the box. What is the probability that the chosen chocolate has a hard centre? 10. A bag contains 30 pieces of Lego. Eight are coloured red, ten are coloured yellow and the rest are black. Jim draws out one piece of Lego. What is the probability that the colour of this piece is red? black? white? not yellow? a. b. c. d. 11. Rita chooses a month at random from the 12 months of the year. What is the probability that the chosen month a. begins with the letter J ? b. begins with a vowel? 12. A day is choosen at random from the month July. What is the probability that the date of this day a. is even? b. will divide by 10 ? c. will divide by 4 and by 6 ? 13. One letter is chosen at random from the letters in the word SCHOOL. What is the probability that it is O ? 14. The students of form 7K are raffling an iced cake to raise money for Christmas decorations. They sell 250 tickets at 5 p. each. Charles bought five tickets. What is the probability that he wins the cake? 15. In a class there are 12 girls and 14 boys. One person is chosen at random. What is the probability that the person chosen is a. a girl? b. a boy? 16. a. b. c. d. 17. 18. 19. A number is chosen from the first 12 positive integers. What is the probability that the chosen number is less than 10 ? at least 5 ? not smaller than 8 ? a two-digit number? Jane rolls a six-sided die. What is the probability that she rolls a. a minimum of 1 ? b. a number between 2 and 5 ? c. a triangular number ? a two-digit number? A book of 150 pages has 30 pages with a picture on it. If one page is chosen at random, what is the probability that it has not a picture on it? One letter is chosen at random from the letters of the alphabet. What is the probability that the letter chosen is a consonant? 20. a. b. c. d. e. 21. a. b. c. d. e. A box contains coloured balls each with one number on them. There are four red balls with the numbers 2, 4, 5 and 6 ; two blue balls with the numbers 1 and 4 ; three green balls with the numbers 3, 5 and 6. Stuart picks at random one ball from the box. Draw the box and each of the balls (use colouring pencils). What is the probability that Stuart picks a green ball? a ball with the number 4 on it? a blue ball with the number 1 on it? a ball of the colour red or with a 5 on it? To play roulette, one spins the wheel clock wise and rolls the ball anti-clock wise. After a minute or so the ball falls into a pocket with a number on it. The numbers on a roulette wheel go from 0 to 36 ; zero is neither an even number or an odd number. A roulette wheel is spun and the ball is rolled. What is the probability that the ball will end up in the pocket with number 24 ? a pocket with an odd number? a pocket with a number which is not odd? a pocket with a prime number? a pocket with a cube number? 22. One letter is chosen at random from the letters in the word AFFECTIONATE. What is the probability that it is a. a vowel? b. a consonant? c. one of the first six letters of the alphabet? 23. A number is chosen at random from the first hundred positive integers. a. Draw a 1010 grid with the numbers 1 to 100. What is the probability that the number chosen is divisible by b. 3 or 4? c. 3 and 4? d. 24. e. A bag of sweets contains 4 caramels, 3 fruit centres, 5 mints and 4 cola bottles. a. b. c. d. e. If one sweet is taken out, what is the probability that it is a mint? a caramel? not a fruit centre? a mint or a cola bottle? a caramel and a mint? 25. a. b. c. d. 26. An 8-sided die is numbered 0 , 0 , 0 , 1 , 1 , 1 , 1 , 2 . The die is rolled once. What is the probability of a. rolling a 0 ? b. not rolling a 2 ? 27. a. b. c. d. 28. a. b. c. d. e. f. g. h. 29. A box of chocolates contains 4 soft centres, 3 nuts, 1 plain chocolate and 2 toffees. Freda takes one chocolate without looking. Give your answers on the following questions in three different ways: as a fraction, as a decimal and as a percentage. What is the probability that she takes a soft centre? a toffee? a nut? a plain chocolate? Fifteen chocolates are put into a bag. Eight of the chocolates are milk, four of the chocolates are plain and the remainder are white. Suzanne selects a chocolate from the bag at random. Calculate the probability that this chocolate will be white not white neither milk nor white either white or plain On a book shelve there are 36 books all novels and cartoons. Of those books 18 are in English, 12 in French and 6 in German. The English books consist of 14 novels and 4 cartoons, there are 3 French novels and there is only 1 German cartoon. Draw a 23 table that shows the given information systematically. Maria takes one book, at random, from the shelve. What is the probability that she takes an English book? a cartoon? a German novel? a book which is either a novel or a French book? a book which is neither a cartoon nor an English book If the book picked by Maria is a French book, what is the probability that it is a novel? If the book picked by Maria is a cartoon, what is the probability that it is in German? In a game of Bingo, the numbers 1 to 90 are drawn out of a bag one at a time. David bought one card which is shown on the right. 3 21 32 63 70 15 24 46 54 76 19 28 37 58 89 What is the probability that the first number to be drawn is on David’s card? 30. At a school fete students can play LUCKY SPINNER for 15p per game. The diagram on the right shows the unbiased lucky spinner used for the game. It consists of eight equal sectors. The spinner is spun once and, when it stops, the arrow points at the amount of money the player gets paid out. What is the probability that after one game a player a. makes a profit? b. makes a loss? c. breaks even? 31. 0p 25p 15p 10p 10p 15p 50p 0p A bag containing Scrabble letters has the following letter distribution a. b. c. d. e. f. g. 32. a. b. c. d. e. f. g. h. A B C D E F G H I J K L M 9 2 2 4 12 2 3 2 9 1 1 4 2 N O P Q R S T U V W X Y Z 6 8 2 1 6 4 6 4 2 2 1 2 1 The first letter is chosen at random from the bag. Find the probability that the chosen letter is an E. in the first half of the alphabet. in the second half of the alphabet. a vowel. a consonant. the only one of its kind. If the chosen letter is a vowel, what is the probability that it is an A? In a certain class of 30 primary school children there are 16 girls. There are 7 girls and 6 boys with fair hair. Draw a 22 table that shows the given information systematically. A pupil is picked at random to be a class captain. Find the probability that the class captain is a girl whose hair is not fair is a boy with fair hair has not got fair hair is a girl and has not got fair hair is a boy or has fair hair If the chosen class captain is a boy, what is the probability that he has fair hair? If the chosen class captain has fair hair, what is the probability that the captain is a girl? 33. The nests of 40 birds are surveyed early in the breading season. The results are: Number of eggs 1 2 3 4 5 a. b. c. d. 34. a. b. c. d. e. f. g. h. i. j. k. Blackbird 2 5 9 2 1 Thrush 4 9 8 0 0 One of these nests is visited at random. What is the probability that it is a blackbird’s nest? of the nest having exactly 3 eggs? If the nest visited is a blackbird’s, what is the probability that it contains 2 eggs? If the nest visited contains 2 eggs, what is the probability that it is a blackbird’s? The integers from 1 to 20 (inclusive) are written on seperate identical cards and the cards are then thoroughly shuffled. Draw a 45 grid with the integers 1 to 20 and circle the square numbers. A card is chosen at random. Find the probability that the number on the card is even odd square both odd and square neither odd nor square either odd or square both even and odd either even or odd If the number on the chosen card is odd, what is the probability that it is square? If the number on the chosen card is square, what is the probability that it is odd?