1. Marble Mania A marble is chosen at random from a bag containing 10 marbles, numbered from 1 to 10 inclusive. Find the probability that the marble chosen is: A marble is chosen at random from a bag containing 10 marbles, numbered from 1 to 10 inclusive. Find the probability that the marble chosen is: - Less than 3 - Not 8 - Odd - At least 7 - A factor of 10 - A prime number

2. A letter is chosen at random. Calculate the probability that the letter selected is A letter is chosen at random. Calculate the probability that the letter selected is A vowel A vowel A consonant A consonant Before g in the alphabet Before g in the alphabet After w in the alphabet After w in the alphabet Between i and o inclusive in the alphabet Between i and o inclusive in the alphabet One of the letters in the word ‘mathematics’ One of the letters in the word ‘mathematics’ Letters

3. Dart Board When a dart is thrown at a dartboard it hits a number between 1 and 20 inclusive. If it is equally likely to hit any of the 20 numbers, calculate the probability that the number hit is When a dart is thrown at a dartboard it hits a number between 1 and 20 inclusive. If it is equally likely to hit any of the 20 numbers, calculate the probability that the number hit is A multiple of 3 A multiple of 3 A factor of 20 A factor of 20 A prime number A prime number

4. Random Letters Giulia chooses a letter at random from the word ‘computer’. Calculate the probability that the letter selected is: Giulia chooses a letter at random from the word ‘computer’. Calculate the probability that the letter selected is: A vowel A vowel Before k in the alphabet Before k in the alphabet Not p Not p

5. More Random Letters Jack selects a letter at random from the word ‘mathematics’. What is the probability that he chooses Jack selects a letter at random from the word ‘mathematics’. What is the probability that he chooses The letter i The letter i A consonant A consonant Either m or a Either m or a

6. A pack of 52 cards is thoroughly shuffled and one card is drawn. What is the probability that the card drawn is A pack of 52 cards is thoroughly shuffled and one card is drawn. What is the probability that the card drawn is An ace An ace The jack of clubs The jack of clubs A diamond A diamond Not a spade Not a spade A heart or club A heart or club A 6 or less (ignore aces) A 6 or less (ignore aces) Cards

7. Pencil case A pencil-case contains two green, four red, five blue and three black ballpoint pens. One pen is chosen at random from the case. What is the probability that the pen chosen is A pencil-case contains two green, four red, five blue and three black ballpoint pens. One pen is chosen at random from the case. What is the probability that the pen chosen is Red Red Not blue Not blue Blue or black Blue or black Orange Orange

8. Spinner Liam and Rikki decide to spin a disc marked with the numbers 1, 2, 3, 4, 5 and 6. Find the probability that the number obtained is Liam and Rikki decide to spin a disc marked with the numbers 1, 2, 3, 4, 5 and 6. Find the probability that the number obtained is 2 2 3 3 Odd Odd A factor of 6 A factor of 6

9. Aimee and Melanie toss two coins at the same time. The first coin is marked with a 3 on one side and a 5 on the other. The second coin is marked with a 2 on one side and a 4 on the other. Find the probability that the total of the two numbers is Aimee and Melanie toss two coins at the same time. The first coin is marked with a 3 on one side and a 5 on the other. The second coin is marked with a 2 on one side and a 4 on the other. Find the probability that the total of the two numbers is 5 5 7 or less 7 or less 8 8 Odd Odd Coin Toss

10. Calendar for June. If a day is selected from this month at random, calculate the probability that the day chosen is: If a day is selected from this month at random, calculate the probability that the day chosen is: A Monday A Monday Not a Friday Not a Friday A Saturday or a Sunday A Saturday or a Sunday Even-numbered Even-numbered A prime-numbered Sunday A prime-numbered Sunday SunMonTueWedThuFriSat 12 3456789 10111213141516 17181920212223 24252627282930

11. It’s a party! Luzie has three invitations to send out for her party – to Mr A, Mrs B and Miss C. She addresses three envelopes for A, B, and C and then leaves the room. As a practical joke Sarah shuffles the invitations and places them at random into the envelopes. What is the probability that Luzie has three invitations to send out for her party – to Mr A, Mrs B and Miss C. She addresses three envelopes for A, B, and C and then leaves the room. As a practical joke Sarah shuffles the invitations and places them at random into the envelopes. What is the probability that Everybody receives an invitation addressed to themselves Everybody receives an invitation addressed to themselves Nobody receives an invitation addressed to themselves Nobody receives an invitation addressed to themselves

12. Taxi Company David, Ryan and Chris jointly own a taxi, which they take turns to drive continuously during the day. The arrangement is that they share the driving in the ratio 2 : 5 : 3 respectively. David, Ryan and Chris jointly own a taxi, which they take turns to drive continuously during the day. The arrangement is that they share the driving in the ratio 2 : 5 : 3 respectively. If you make arrangements to hire the taxi at randomly chosen time, what is the probability that Ryan will be the driver? If you make arrangements to hire the taxi at randomly chosen time, what is the probability that Ryan will be the driver?

13. Rosie’s Sweets Rosie makes jelly-beans in several colours: red, orange, pink, purple, blue, green, white, yellow and black. A mixing machine fills packets with these colours according to a pre-set ratio, which is Rosie makes jelly-beans in several colours: red, orange, pink, purple, blue, green, white, yellow and black. A mixing machine fills packets with these colours according to a pre-set ratio, which is 3 : 2 : 4 : 2 : 1 : 3 : 2 : 5 : 3 for each colour respectively. If a jelly-bean is chosen at random from a packet, calculate the probability that a black one is selected. for each colour respectively. If a jelly-bean is chosen at random from a packet, calculate the probability that a black one is selected.

14. Cards Six cards are marked with numbers on one side and the other side is blank. The numbers on the cards are 2, 4, 5, 7, 11 and 13. The cards are shuffled, and two cards are chosen and turned face up. Calculate the probability that the numbers (hint: write down all the possible combinations – there are 15) Six cards are marked with numbers on one side and the other side is blank. The numbers on the cards are 2, 4, 5, 7, 11 and 13. The cards are shuffled, and two cards are chosen and turned face up. Calculate the probability that the numbers (hint: write down all the possible combinations – there are 15) Are both odd Are both odd Are both less than 10 Are both less than 10 Have a sum of 18 Have a sum of 18

15. Socks Yuka has two different pairs of socks. She washes them, and pairs them up again at random. Calculate the probability that both pairs of socks are matching. Yuka has two different pairs of socks. She washes them, and pairs them up again at random. Calculate the probability that both pairs of socks are matching.

17. Marble Mania Answers A marble is chosen at random from a bag containing 10 marbles, numbered from 1 to 10 inclusive. Find the probability that the marble chosen is: A marble is chosen at random from a bag containing 10 marbles, numbered from 1 to 10 inclusive. Find the probability that the marble chosen is: 1/5 - Less than 3 - Not 8 - Odd - At least 7 - A factor of 10 - A prime number 9/10 2/5 1/2 2/5

18. A vowel A vowel A consonant A consonant Before g in the alphabet Before g in the alphabet After w in the alphabet After w in the alphabet Between i and o inclusive in the alphabet Between i and o inclusive in the alphabet One of the letters in the word ‘mathematics’ One of the letters in the word ‘mathematics’ 5/26 21/26 3/13 3/26 7/26 4/13 A letter is chosen at random. Calculate the probability that the letter selected is A letter is chosen at random. Calculate the probability that the letter selected is Letters Answers

19. Dart Board ANSWERS Assume that when a dart is thrown at a dartboard it hits a number between 1 and 20 inclusive. If it is equally likely to hit any of the 20 numbers, calculate the probability that the number hit is Assume that when a dart is thrown at a dartboard it hits a number between 1 and 20 inclusive. If it is equally likely to hit any of the 20 numbers, calculate the probability that the number hit is A multiple of 3 A multiple of 3 A factor of 20 A factor of 20 A prime number A prime number 3/10 2/5

20. Random Letters ANSWERS Giulia chooses a letter at random from the word ‘computer’. Calculate the probability that the letter selected is: Giulia chooses a letter at random from the word ‘computer’. Calculate the probability that the letter selected is: A vowel A vowel Before k in the alphabet Before k in the alphabet Not p Not p 3/8 1/4 7/8

21. More Random Letters ANSWERS Jack selects a letter at random from the word ‘mathematics’. What is the probability that he chooses Jack selects a letter at random from the word ‘mathematics’. What is the probability that he chooses The letter i The letter i A consonant A consonant Either m or a Either m or a 1/11 7/11 4/11

22. A pack of 52 cards is thoroughly shuffled and one card is drawn. What is the probability that the card drawn is ANSWERS A pack of 52 cards is thoroughly shuffled and one card is drawn. What is the probability that the card drawn is ANSWERS An ace An ace The jack of clubs The jack of clubs A diamond A diamond Not a spade Not a spade A heart or club A heart or club A 6 or less (ignore aces) A 6 or less (ignore aces) 1/13 1/52 1/4 3/4 1/2 5/13 Cards Answers

23. Pencil case ANSWERS A pencil-case contains two green, four red, five blue and three black ballpoint pens. One pen is chosen at random from the case. What is the probability that the pen chosen is A pencil-case contains two green, four red, five blue and three black ballpoint pens. One pen is chosen at random from the case. What is the probability that the pen chosen is Red Red Not blue Not blue Blue or black Blue or black 2/7 9/14 4/7 Orange Orange0

24. Liam and Rikki decide to spin a disc marked with the numbers 1, 2, 3, 4, 5 and 6. Find the probability that the number obtained is Liam and Rikki decide to spin a disc marked with the numbers 1, 2, 3, 4, 5 and 6. Find the probability that the number obtained is 2 2 3 3 Odd Odd 1/8 1/4 5/8 A factor of 6 A factor of 65/8 Spinner Answers

25. Aimee and Melanie toss two coins at the same time. The first coin is marked with a 3 on one side and a 5 on the other. The second coin is marked with a 2 on one side and a 4 on the other. Find the probability that the total of the two numbers is Aimee and Melanie toss two coins at the same time. The first coin is marked with a 3 on one side and a 5 on the other. The second coin is marked with a 2 on one side and a 4 on the other. Find the probability that the total of the two numbers is 5 5 7 or less 7 or less 8 8 1/4 3/4 0 Odd Odd1 Coin Toss Answers

26. Calendar ANSWERS A Monday A Monday Not a Friday Not a Friday A Saturday or a Sunday A Saturday or a Sunday 2/15 5/6 3/10 Even-numbered Even-numbered1/2 A prime-numbered Sunday A prime-numbered Sunday1/15 SunMonTueWedThuFriSat 12 3456789 10111213141516 17181920212223 24252627282930

27. It’s a party! ANSWERS Luzie has three invitations to send out for her party – to Mr A, Mrs B and Miss C. She addresses three envelopes for A, B, and C and then leaves the room. As a practical joke Sarah shuffles the invitations and places them at random into the envelopes. What is the probability that Luzie has three invitations to send out for her party – to Mr A, Mrs B and Miss C. She addresses three envelopes for A, B, and C and then leaves the room. As a practical joke Sarah shuffles the invitations and places them at random into the envelopes. What is the probability that 1/6 1/3 Everybody receives an invitation addressed to themselves Everybody receives an invitation addressed to themselves Nobody receives an invitation addressed to themselves Nobody receives an invitation addressed to themselves

28. Taxi Company ANSWERS David, Ryan and Chris jointly own a taxi, which they take turns to drive continuously during the day. The arrangement is that they share the driving in the ratio 2 : 5 : 3 respectively. David, Ryan and Chris jointly own a taxi, which they take turns to drive continuously during the day. The arrangement is that they share the driving in the ratio 2 : 5 : 3 respectively. If you make arrangements to hire the taxi at randomly chosen time, what is the probability that Ryan will be the driver? If you make arrangements to hire the taxi at randomly chosen time, what is the probability that Ryan will be the driver? Answer: 1/2

29. Rosie’s Sweets ANSWERS Rosie makes jelly-beans in several colours: red, orange, pink, purple, blue, green, white, yellow and black. A mixing machine fills packets with these colours according to a pre-set ratio, which is Rosie makes jelly-beans in several colours: red, orange, pink, purple, blue, green, white, yellow and black. A mixing machine fills packets with these colours according to a pre-set ratio, which is 3 : 2 : 4 : 2 : 1 : 3 : 2 : 5 : 3 for each colour respectively. If a jelly-bean is chosen at random from a packet, calculate the probability that a black one is selected. for each colour respectively. If a jelly-bean is chosen at random from a packet, calculate the probability that a black one is selected. Answer: 3/25

30. Cards ANSWERS Six cards are marked with numbers on one side and the other side is blank. The numbers on the cards are 2, 4, 5, 7, 11 and 13. The cards are shuffled, and two cards are chosen and turned face up. Calculate the probability that the numbers (hint: write down all the possible combinations – there are 15) Six cards are marked with numbers on one side and the other side is blank. The numbers on the cards are 2, 4, 5, 7, 11 and 13. The cards are shuffled, and two cards are chosen and turned face up. Calculate the probability that the numbers (hint: write down all the possible combinations – there are 15) Are both odd Are both odd Are both less than 10 Are both less than 10 Have a sum of 18 Have a sum of 18 2/5 2/15

31. Socks ANSWERS Yuka has two different pairs of socks. She washes them, and pairs them up again at random. Calculate the probability that both pairs of socks are matching. Yuka has two different pairs of socks. She washes them, and pairs them up again at random. Calculate the probability that both pairs of socks are matching. Answer: 1/3