1. Probability 1 4 2 6 8 9 3 5 7 1 Vocabulary:
probability sample space chance
likelihood certain likely
equally likely unlikely event
outcome experiment theoretical
spinner die dice
favourable fair bias
random complement 2 6 8 9 3 5 7 1

2. Probability 1 3 Basic Concepts:
Determine the number of outcomes in an experiment
Creating lists to count the number of outcomes
Simple probability calculations
Estimate relative frequencies and use them to estimate probabilities
Express probabilities using fractions, decimals and percentages
Understand that probabilities always lie between 0 and 1
Illustrate experiment results using graphs and tables
Use the complement of an event to easily find probability.

3. What is Probability?
Probability is the study of chance, or how likely something is to happen. Probabilities range from 0 (an impossible event) to 1 (a certain event). If things have an equal chance of happening, we call them equally likely outcomes. This continuum shows where probabilities fall:
On the continuum, place in the correct positions:
likely unlikely very unlikely certain
Impossible very likely equally likely 2 5 4 11 13 3 6 10 14 1 15 8 7 9 12

6. Sample Space
The sample space is a list of all possible outcomes. For a coin, we say the sample space is {heads, tails}, because there is no other possible outcome. 2 5 4 11 13 3 6 10 14 1 15 8 7 9 12

8. Multistage events
In the language of chance, an event is an outcome or a collection of outcomes.
For example, when a die is rolled, ‘getting a 2’ is one of the six equally likely outcomes. The event is ‘getting a 2’.
‘Getting an even number’ includes the outcomes 2, 4 or 6. This event is a collection of outcomes.
A multistage event is one that is made up of simpler events. When finding the sample space for multistage events, it is often useful to use a systematic method such as a list, table or tree diagram. 2 5 4 11 13 3 6 10 14 1 15 8 7 9 12

13. Counting Items
The fundamental counting theorem states:
The total number of outcomes for a multistage event can be determined from the product of the number of choices at each stage. 2 5 4 11 13 3 6 10 14 1 15 8 7 9 12

18. 2 5 4 3 6 1 8 7 9 Theoretical Probability
A pail contains eight red marbles, five blue marbles, six green marbles and three yellow marbles. If a single marble is chosen from the pail, what is the probability it will be red? Blue? Green?
𝑃 𝑅𝑒𝑑 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑒𝑑 𝑚𝑎𝑟𝑏𝑙𝑒𝑠 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑎𝑟𝑏𝑙𝑒𝑠
= 8 22
𝑃 𝐵𝑙𝑢𝑒 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑙𝑢𝑒 𝑚𝑎𝑟𝑏𝑙𝑒𝑠 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑎𝑟𝑏𝑙𝑒𝑠 =
𝑃 𝐺𝑟𝑒𝑒𝑛 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑔𝑟𝑒𝑒𝑛 𝑚𝑎𝑟𝑏𝑙𝑒𝑠 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑎𝑟𝑏𝑙𝑒𝑠 2 5 4 11 13 3 6 10 14 1 15 8 7 9 12

25. The complement
The sum of the probabilities of all possible outcomes of a simple event is always 1. This can be used to simplify calculations (it is called using the complement). 2 5 4 11 13 3 6 10 14 1 15 8 7 9 12