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Chance and Probability

SERIES TOPIC

1G 1

Reuben is going to put ten blocks in a bag and ask a friend to choose one without looking. Tick the blocks he could put in the bag to make the probability of choosing a cube

2 10 .

What is the probability of spinning a striped segment on each of these wheels? Write your answer as a rating between 0 and 1 using decimals.

Probability measures how likely something is to happen. Events that are certain to happen are given a probability of 1. Events that will never happen are given a probability of 0. Events that could happen are rated between 0 and 1.

EventProbability

as a fractionProbability

as a decimal

When you flip a coin, it will land on heads.

You will grow wings and fly today.

A spinner with 10 even segments with the numbers 1 to 10 will land on 3.

5 people are lined up and every second person in the line has gloves on. What is the chance that one person is not wearing gloves?

You have 20 cards. 5 have hearts, 5 have stripes and the rest are blank. What is the chance you will choose a blank card?

Chance and probability – probability scale

1

2

3

a b c d

Probability measures how likely something is to happen.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

impossible even certain

likelyunlikely

0 10

1 10

2 10

3 10

4 10

5 10

6 10

7 10

8 10

9 10

10 10

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Chance and Probability

SERIES TOPIC

2 G 1

Sam did an experiment with 10 cubes that were either red, white or blue. She took a cube from a jar without looking, tallied which colour it was then put it back in the same jar. She repeated the process 20 times. After tallying her results, she created this pie chart to show the results of the experiment.

Inside a box there are 3 rectangles, 2 triangles and 5 squares. Without looking, Ellie chooses one shape from the box.

a Write A for a triangle, B for a square and C for a rectangle on this probability scale to show the probability of Ellie choosing each type of shape.

b 3 more rectangles, 2 more triangles and 5 more squares are added to the same box. Use the same letters on this probability scale to show the probability of Ellie choosing each shape from the box.

c What do you notice? ___________________________________________________________________

Chance and probability – probability scale

100 guests each buy a ticket for a raffle at a fundraising dinner. The winning ticket will be selected at random. This table on the right shows the colours of all of the tickets in the raffle.

What is the probability of the winning ticket being red, purple or orange? put a x on this probability scale to show the probability of each colour and write the colour beneath the x.

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

a How many times did Sam take each colour out of the jar? Remember she performed the experiment 20 times.

Red

White

Blue

b Draw the combination of cubes there could have been inside the jar. Remember there are only 10 cubes.

WhiteRed

Blue

Red 10Purple 40Orange 50

Total 100

On a piece of paper or in your workbook

SERIES TOPIC

F 12Copyright © 3P Learning

Data Representation

In a scandal that rocked the school, it was found that ticket sales data were fudged. The maximum attendees for any one week was actually 60.

a How many tickets does each symbol now represent?

b How many tickets were really sold during the entire sales period?

Types of graphs 1 – picture graphs

5F put on their own version of “So You Think You Can Dance”. Use the graph and key to answer the following:

Ticket Sales Key: = 20 tickets

Week 1

Week 2

Week 3

Week 4

Week 5

a How many tickets does each represent?

b How many tickets were sold in Week 1?

c How many tickets were sold in Week 5?

d In which week were the most tickets sold?

e How many tickets were sold that week?

f During which two weeks were the same number of tickets sold?

g How many more tickets were sold in Week 3 than Week 1?

h How many tickets were sold during the entire sales period?

3

4

SERIES TOPIC

5F 1Copyright © 3P Learning

Data Representation 1

b What are some key issues on the graph you’d point out? Work in a small team to come up with a solution. Pretend your teacher or another group is the principal and present your case.

Types of graphs 1 – column graphs

The after care kids are staging a mutiny. They are over watching the same DVDs and making popcorn every day and want to do something new and exciting on Wednesdays. This table shows the activities they’d prefer.

a Help them present a case to the principal by completing the column graph:

4Activity

Number of Students

No change 1Swimming 30Art 11Football 18Dancing 23

Name your graph and both axes

Label each column Select and label an

appropriate scale

SERIES TOPIC

7FCopyright © 3P Learning

Data Representation 2

A group of students was surveyed to find out what they spend their pocket money on. This pie chart shows the results. Circle True or False next to each statement.

a More than half the students surveyed spent their money on a mobile phone.True / False

b 4

20 surveyed spent their money on food.

True / False

c 20 students were surveyed in total.True / False

Colour and label this pie chart according to the information in the table:

A pie chart, also known as a sector graph, shows data as parts of a whole. The circle represents the total amount while the segments are the parts. When we compare the parts to the whole, we’re looking at proportion. This is often written as a fraction.

Types of graphs 2 – pie charts

1

2

Toys1

Mobile phone

12

Music4

Food3

Category Amount Fraction

Red 3

Blue 2

Yellow 5

Total

What do students spend their pocket money on?

This pie chart shows the favourite ice cream flavours of 10 people.

Favourite ice cream flavours of 10 people

The table below summarises the information displayed on this graph.

Category Amount Fraction

Vanilla 33

10

Strawberry 22

10

Mango 11

10

Choc-chip 44

10

Total 101010

Choc-chip4

Vanilla3

Strawberry2

Mango1

Favourite colours of 10 peopleDraw this on paper to complete if not able to print out

Registered School: Wyrallah Road Public School (EAST LISMORE NSW)

Copyright © 2019 Australasian Problem Solving Mathematical Olympiads (APSMO) Inc. and Mathematical Olympiads for Elementary and Middle Schools. All rights reserved.

OLYMPIAD

4APSMO2019 : DIVISION J

WEDNESDAY 21 AUGUST 2019

4A. Suggested Time: 3 minutesWhat is the value of 2019 - 219 - 192 - 921?

4B. Suggested Time: 5 minutesStarting with 46, and adding the same amount each time, results in the sequence 46, 53, 60, 67, and so on.What is the 25th number in the sequence?

4C. Suggested Time: 5 minutesEthan is thinking of a four-digit counting number.The thousands digit is different to the hundreds digit.The hundreds digit, the tens digit, and the ones digit are the same. The sum of the digits is 28.Ethan’s number is prime. What is Ethan’s number?

4D. Suggested Time: 6 minutes Each person has some information about a secret number.• Amelia knows that the secret number is exactly divisible by 9.• Blake knows that the secret number is a 3-digit number with

digits appearing in increasing order.• Chelsea knows that the difference between the last and middle

digits does not equal the difference between the middle and first digits.

• Daniel knows that neither 1 nor 9 is used anywhere as a digit.What is the secret number?

4E. Suggested Time: 7 minutesThis structure is made up of unit cubes.The bottom layer is a 3 × 3 square of unit cubes.The middle layer is a 2 × 2 square of unit cubes.The top layer is a single unit cube. How many square units are in the surface area of this structure?

Total Time Allowed: 30 Minutes

Write your answers in the boxes on the back.

Keep your answers hidden by folding backwards on this line.

←

Registered School: Wyrallah Road Public School (EAST LISMORE NSW)

Copyright © 2019 Australasian Problem Solving Mathematical Olympiads (APSMO) Inc. and Mathematical Olympiads for Elementary and Middle Schools. All rights reserved.

OLYMPIAD

4APSMO2019 : DIVISION J

WEDNESDAY 21 AUGUST 2019

4A.

4B.

4C.

4D.

4E.

Student Name:

Fold here. Keep your answers hidden.