G7_Probability 1

​Learning Objectives

• use the language associated with probability

• understand how the probabilities range from 0 to 1​

• ​learn how to identify mutually exclusive outcomes

• use equally likely outcomes to find theoretical probabilities.

Open Ended

If you throw a dice, write the possible outcome/result!

​Introduction

​Uncertainty and chance exist in many situations in real life.

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For example, if you are planning an outdoor activity, it is important to know what type of weather to expect. Will it be sunny? Will it be windy? Will it rain?

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You cannot be certain what the weather will be. However, a weather forecast often gives you an idea of what type of weather to expect.

​The branch of Mathematics that deals with uncertainty is called probability.

In this unit you will learn how to calculate and use probabilities in simple situations.

13.1 The probability scale

​Rolling an odd number on a dice or winning a football match are examples of events.

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Events can have a number of different outcomes.

The outcomes that give an odd number when you roll a dice are 1, 3 and 5.

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You can use words such as certain, likely, unlikely and impossible to describe the likelihood that an event will happen.

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You can also use a number between 0 and 1 to represent the likelihood that an event will happen. This number is called a probability.

13.1 The probability scale

​You can write a probability as a fraction, a decimal or a percentage.

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For example, an even chance means a probability of 0.5 or 1/2 or 50%.

Multiple Choice

Tigers and Lions are two football teams.

The probability that Tigers will win their next match is 45%.

The probability that Lions will win their next match is $$\frac{4}{5}$$  .

Which team is more likely to win their next match?

• Tigers

• Lions

Multiple Choice

An example of a certain event is when Monday:

• is holiday

• follows Sundays

Multiple Choice

The red dot on this number line could show the chance of:

• throwing a 4 on a normal dice

• a tossed coin landing heads up

Multiple Choice

Which of these events is most likely to happen?

• A football hitting a window breaks the window.

• A table tennis ball hitting a window breaks the window.

Multiple Choice

The weather broadcast states that the probability of rain for tomorrow is 80%.

This means that:

• rain is certain

• rain is likely

• rain is unlikely

• there is an equal chance of there being rain or no rain

13.1 Mutually exclusive outcomes

​When two outcomes cannot happen at the same time they are mutually exclusive.

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For example, if you get a 1 when you throw a dice, you cannot also get a 3.​

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​When you roll a dice, each number is equally likely. 1, 2, 3, 4, 5 and 6 are equally likely outcomes.

Remember !!!

Example 1

Example 2

​a. 2?

​b. 3?

​c. 5?

​d. 8?

​e. 9?

Example 2

​a. 2?

​b. 3?

​c. 5?

​d. 8?

​e. 9?

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​Solution:

Multiple Choice

What is the probability of spinning a 2 on the spinner?

• 1/2

• 1/3

• 1/8

• 1/4

Multiple Choice

What is the probability the spinner stops on yellow?

• .075

• 50%

• 25%

• 3/8

Multiple Choice

A die is rolled. What is the probability that the result is less than 3 ?

• 1/2
• 1/3
• 1/4
• 1/6

Multiple Choice

Find the probability of rolling a 7 on a single die.

• 1/6

• 7/6

• 0

• 7/7

Multiple Choice

The letters that form the word ALGEBRA are placed in a bowl. What is the probability of choosing a letter other than “A”? 

• 2/7
• 5/49
• 5/7
• 10/49