Marble Mania Marble Mania A marble is chosen at random from a A marble is chosen at random from a

bag containing 10 marbles, numbered bag containing 10 marbles, numbered from 1 to 10 inclusive. Find the from 1 to 10 inclusive. Find the probability that the marble chosen is:probability that the marble chosen is:

- Less than 3- Less than 3

- Not 8- Not 8

- Odd

- At least 7

- A factor of 10

- A prime number

A letter is chosen at random. Calculate A letter is chosen at random. Calculate the probability that the letter selected isthe probability that the letter selected is

• A vowelA vowel

• A consonantA consonant

• Before g in the alphabetBefore g in the alphabet

• After w in the alphabetAfter w in the alphabet

• Between i and o inclusive in the alphabetBetween i and o inclusive in the alphabet

• One of the letters in the word One of the letters in the word ‘mathematics’‘mathematics’

LettersLetters

Dart BoardDart Board

When a dart is thrown at a dartboard When a dart is thrown at a dartboard it hits a number between 1 and 20 it hits a number between 1 and 20 inclusive. If it is equally likely to hit inclusive. If it is equally likely to hit any of the 20 numbers, calculate the any of the 20 numbers, calculate the probability that the number hit isprobability that the number hit is

• A multiple of 3A multiple of 3

• A factor of 20A factor of 20

• A prime numberA prime number

Random LettersRandom Letters

Giulia chooses a letter at random from Giulia chooses a letter at random from the word ‘computer’. Calculate the the word ‘computer’. Calculate the probability that the letter selected is:probability that the letter selected is:

• A vowelA vowel

• Before k in the Before k in the alphabetalphabet• Not pNot p

More Random LettersMore Random Letters

Jack selects a letter at random from Jack selects a letter at random from the word ‘mathematics’. What is the the word ‘mathematics’. What is the probability that he choosesprobability that he chooses

• The letter iThe letter i

• A consonantA consonant

• Either m or aEither m or a

A pack of 52 cards is thoroughly shuffled A pack of 52 cards is thoroughly shuffled and one card is drawn. What is the and one card is drawn. What is the probability that the card drawn isprobability that the card drawn is

• An aceAn ace

• The jack of The jack of clubsclubs• A diamondA diamond

• Not a spadeNot a spade

• A heart or clubA heart or club

• A 6 or less (ignore A 6 or less (ignore aces)aces)

CardsCards

Pencil casePencil case

A pencil-case contains two green, four A pencil-case contains two green, four red, five blue and three black ballpoint red, five blue and three black ballpoint pens. One pen is chosen at random pens. One pen is chosen at random from the case. What is the probability from the case. What is the probability that the pen chosen isthat the pen chosen is

• RedRed

• Not blueNot blue

• Blue or Blue or blackblack• OrangeOrange

SpinnerSpinner Liam and Rikki decide to spin a disc marked Liam and Rikki decide to spin a disc marked

with the numbers 1, 2, 3, 4, 5 and 6. Find with the numbers 1, 2, 3, 4, 5 and 6. Find the probability that the number obtained isthe probability that the number obtained is

• 22

• 33

• OddOdd

• A factor of A factor of 66

Aimee and Melanie toss two coins at the Aimee and Melanie toss two coins at the same time. The first coin is marked with a 3 same time. The first coin is marked with a 3 on one side and a 5 on the other. The on one side and a 5 on the other. The second coin is marked with a 2 on one side second coin is marked with a 2 on one side and a 4 on the other. Find the probability and a 4 on the other. Find the probability that the total of the two numbers isthat the total of the two numbers is

• 55

• 7 or less7 or less

• 88

• OddOdd

Coin TossCoin Toss

Calendar for June. Calendar for June. If a day is selected from this month at random, If a day is selected from this month at random,

calculate the probability that the day chosen is:calculate the probability that the day chosen is:

• A MondayA Monday• Not a FridayNot a Friday• A Saturday or a A Saturday or a SundaySunday• Even-numberedEven-numbered• A prime-numbered A prime-numbered SundaySunday

SunSun MonMon TueTue WedWed ThuThu FriFri SatSat

11 22

33 44 55 66 77 88 99

1010 1111 1212 1313 1414 1515 1616

1717 1818 1919 2020 2121 2222 2323

2424 2525 2626 2727 2828 2929 3030

It’s a party!It’s a party!

Luzie has three invitations to send out for her Luzie has three invitations to send out for her party – to Mr A, Mrs B and Miss C. She party – to Mr A, Mrs B and Miss C. She addresses three envelopes for A, B, and C and addresses three envelopes for A, B, and C and then leaves the room. As a practical joke then leaves the room. As a practical joke Sarah shuffles the invitations and places them Sarah shuffles the invitations and places them at random into the envelopes. What is the at random into the envelopes. What is the probability thatprobability that

• Everybody receives an invitation Everybody receives an invitation addressed to themselvesaddressed to themselves

• Nobody receives an invitation Nobody receives an invitation addressed to themselvesaddressed to themselves

Taxi CompanyTaxi Company

David, Ryan and Chris jointly own a taxi, David, Ryan and Chris jointly own a taxi, which they take turns to drive which they take turns to drive continuously during the day. The continuously during the day. The arrangement is that they share the arrangement is that they share the driving in the ratio 2 : 5 : 3 respectively. driving in the ratio 2 : 5 : 3 respectively.

If you make arrangements to hire the If you make arrangements to hire the taxi at randomly chosen time, what is taxi at randomly chosen time, what is the probability that Ryan will be the the probability that Ryan will be the driver?driver?

Rosie’s SweetsRosie’s Sweets

Rosie makes jelly-beans in several Rosie makes jelly-beans in several colours: red, orange, pink, purple, blue, colours: red, orange, pink, purple, blue, green, white, yellow and black. A mixing green, white, yellow and black. A mixing machine fills packets with these colours machine fills packets with these colours according to a pre-set ratio, which is according to a pre-set ratio, which is

3 : 2 : 4 : 2 : 1 : 3 : 2 : 5 : 33 : 2 : 4 : 2 : 1 : 3 : 2 : 5 : 3

for each colour respectively. If a jelly-for each colour respectively. If a jelly-bean is chosen at random from a packet, bean is chosen at random from a packet, calculate the probability that a black one calculate the probability that a black one is selected.is selected.

CardsCards

Six cards are marked with numbers on one Six cards are marked with numbers on one side and the other side is blank. The numbers side and the other side is blank. The numbers on the cards are 2, 4, 5, 7, 11 and 13. The on the cards are 2, 4, 5, 7, 11 and 13. The cards are shuffled, and two cards are chosen cards are shuffled, and two cards are chosen and turned face up. Calculate the probability and turned face up. Calculate the probability that the numbers (hint: write down all the that the numbers (hint: write down all the possible combinations – there are 15)possible combinations – there are 15)

• Are both oddAre both odd

• Are both less than 10Are both less than 10

• Have a sum of 18Have a sum of 18

SocksSocks

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

Marble Mania Marble Mania Answers Answers

A marble is chosen at random from a A marble is chosen at random from a bag containing 10 marbles, numbered bag containing 10 marbles, numbered from 1 to 10 inclusive. Find the from 1 to 10 inclusive. Find the probability that the marble chosen is:probability that the marble chosen is:

1/5- Less than 3- Less than 3

- Not 8- Not 8

- Odd

- At least 7

- A factor of 10

- A prime number

9/10

2/5

1/2

2/5

2/5

• A vowelA vowel

• A consonantA consonant

• Before g in the alphabetBefore g in the alphabet

• After w in the alphabetAfter w in the alphabet

• Between i and o inclusive in the alphabetBetween i and o inclusive in the alphabet

• One of the letters in the word One of the letters in the word ‘mathematics’‘mathematics’

5/26

21/26

3/13

3/26

7/26

4/13

A letter is chosen at random. Calculate A letter is chosen at random. Calculate the probability that the letter selected isthe probability that the letter selected is

Letters Letters AnswersAnswers

Dart Board Dart Board ANSWERSANSWERS

Assume that when a dart is thrown at Assume that when a dart is thrown at a dartboard it hits a number between a dartboard it hits a number between 1 and 20 inclusive. If it is equally likely 1 and 20 inclusive. If it is equally likely to hit any of the 20 numbers, calculate to hit any of the 20 numbers, calculate the probability that the number hit isthe probability that the number hit is

• A multiple of 3A multiple of 3

• A factor of 20A factor of 20

• A prime numberA prime number

3/10

3/10

2/5

Random Letters Random Letters ANSWERSANSWERS Giulia chooses a letter at random from Giulia chooses a letter at random from

the word ‘computer’. Calculate the the word ‘computer’. Calculate the probability that the letter selected is:probability that the letter selected is:

• A vowelA vowel

• Before k in the Before k in the alphabetalphabet• Not pNot p

3/8

1/4

7/8

More Random Letters More Random Letters ANSWERSANSWERS Jack selects a letter at random from Jack selects a letter at random from

the word ‘mathematics’. What is the the word ‘mathematics’. What is the probability that he choosesprobability that he chooses

• The letter iThe letter i

• A consonantA consonant

• Either m or aEither m or a

1/11

7/11

4/11

A pack of 52 cards is thoroughly shuffled A pack of 52 cards is thoroughly shuffled and one card is drawn. What is the and one card is drawn. What is the probability that the card drawn is ANSWERSprobability that the card drawn is ANSWERS

• An aceAn ace

• The jack of The jack of clubsclubs• A diamondA diamond

• Not a spadeNot a spade

• A heart or clubA heart or club

• A 6 or less (ignore A 6 or less (ignore aces)aces)

1/13

1/52

1/4

3/4

1/2

5/13

Cards Cards AnswersAnswers

Pencil case Pencil case ANSWERSANSWERS

A pencil-case contains two green, four A pencil-case contains two green, four red, five blue and three black ballpoint red, five blue and three black ballpoint pens. One pen is chosen at random pens. One pen is chosen at random from the case. What is the probability from the case. What is the probability that the pen chosen isthat the pen chosen is

• RedRed

• Not blueNot blue

• Blue or Blue or blackblack

2/7

9/14

4/7

• OrangeOrange 0

Liam and Rikki decide to spin a disc Liam and Rikki decide to spin a disc marked with the numbers 1, 2, 3, 4, 5 marked with the numbers 1, 2, 3, 4, 5 and 6. Find the probability that the and 6. Find the probability that the number obtained isnumber obtained is• 22

• 33

• OddOdd

1/8

1/4

5/8

• A factor of A factor of 66

5/8

Spinner Spinner AnswersAnswers

Aimee and Melanie toss two coins at the Aimee and Melanie toss two coins at the same time. The first coin is marked with a 3 same time. The first coin is marked with a 3 on one side and a 5 on the other. The on one side and a 5 on the other. The second coin is marked with a 2 on one side second coin is marked with a 2 on one side and a 4 on the other. Find the probability and a 4 on the other. Find the probability that the total of the two numbers isthat the total of the two numbers is

• 55

• 7 or less7 or less

• 88

1/4

3/4

0

• OddOdd 1

Coin Toss Coin Toss AnswersAnswers

Calendar Calendar ANSWERSANSWERS

• A MondayA Monday• Not a FridayNot a Friday

• A Saturday or a A Saturday or a SundaySunday

2/15

5/6

3/10• Even-numberedEven-numbered 1/2

• A prime-numbered A prime-numbered SundaySunday

1/15

SunSun MonMon TueTue WedWed ThuThu FriFri SatSat

11 22

33 44 55 66 77 88 99

1010 1111 1212 1313 1414 1515 1616

1717 1818 1919 2020 2121 2222 2323

2424 2525 2626 2727 2828 2929 3030

It’s a party! It’s a party! ANSWERSANSWERS Luzie has three invitations to send out for her Luzie has three invitations to send out for her

party – to Mr A, Mrs B and Miss C. She party – to Mr A, Mrs B and Miss C. She addresses three envelopes for A, B, and C and addresses three envelopes for A, B, and C and then leaves the room. As a practical joke then leaves the room. As a practical joke Sarah shuffles the invitations and places them Sarah shuffles the invitations and places them at random into the envelopes. What is the at random into the envelopes. What is the probability thatprobability that

1/6

1/3

• Everybody receives an invitation Everybody receives an invitation addressed to themselvesaddressed to themselves

• Nobody receives an invitation Nobody receives an invitation addressed to themselvesaddressed to themselves

Taxi Company Taxi Company ANSWERSANSWERS David, Ryan and Chris jointly own a taxi, David, Ryan and Chris jointly own a taxi,

which they take turns to drive which they take turns to drive continuously during the day. The continuously during the day. The arrangement is that they share the arrangement is that they share the driving in the ratio 2 : 5 : 3 respectively. driving in the ratio 2 : 5 : 3 respectively.

If you make arrangements to hire the If you make arrangements to hire the taxi at randomly chosen time, what is taxi at randomly chosen time, what is the probability that Ryan will be the the probability that Ryan will be the driver?driver?

Answer: 1/2

Rosie’s Sweets Rosie’s Sweets ANSWERSANSWERS Rosie makes jelly-beans in several Rosie makes jelly-beans in several

colours: red, orange, pink, purple, blue, colours: red, orange, pink, purple, blue, green, white, yellow and black. A mixing green, white, yellow and black. A mixing machine fills packets with these colours machine fills packets with these colours according to a pre-set ratio, which is according to a pre-set ratio, which is

3 : 2 : 4 : 2 : 1 : 3 : 2 : 5 : 33 : 2 : 4 : 2 : 1 : 3 : 2 : 5 : 3

for each colour respectively. If a jelly-for each colour respectively. If a jelly-bean is chosen at random from a packet, bean is chosen at random from a packet, calculate the probability that a black one calculate the probability that a black one is selected.is selected.Answer: 3/25

Cards Cards ANSWERSANSWERS Six cards are marked with numbers on one Six cards are marked with numbers on one

side and the other side is blank. The numbers side and the other side is blank. The numbers on the cards are 2, 4, 5, 7, 11 and 13. The on the cards are 2, 4, 5, 7, 11 and 13. The cards are shuffled, and two cards are chosen cards are shuffled, and two cards are chosen and turned face up. Calculate the probability and turned face up. Calculate the probability that the numbers (hint: write down all the that the numbers (hint: write down all the possible combinations – there are 15)possible combinations – there are 15)

• Are both oddAre both odd

• Are both less than 10Are both less than 10

• Have a sum of 18Have a sum of 18

2/5

2/5

2/15

Socks Socks ANSWERSANSWERS

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

Answer: 1/3