I don’t remember much about probability in high school.  I remember it included using diagrams to work out the possible scenarios and using fractions and percentages to demonstrate the likelihood of it happening.  Although, I cannot remember covering probability in primary school, children begin to explore questions around probability and chance from year one (ACARA, 2015, ACMSP024). 

 

Probability is the concept of chance of an event occurring.  This term is used frequently in statistics as it can be used to estimate an expected frequency.  Probability is useful to apply to situations where the outcome cannot be predetermined.  A lot of events that happen is due to chance.  It is common for businesses to fail or succeed due to unlucky or lucky events.  Probability involves predicting what might happen. It is important to build children’s understanding of probability through exposure to key concept and terms from early age.  This includes discussing events in terms of likelihood it will occur using terms such as likely, unlikely, certain, uncertain and impossible.  Certain and impossible are generally the easiest concepts to master).  However, likely and unlikely are less familiar and require more extensive development.  Students can work through a list of events and categorise its likelihood it will occur (ACARA, 2015, ACMSP024; ACMSP047).  An extension to this activity would be to allow students to develop their own statements and sort them into categories.  Activities that involve spinners, dice and coins are all often used to introduce probability. As students’ knowledge and understanding of probability increase they will be able to conduct experiments and using the data to conduct graphs and tables to answer the questions.  Students by the end of year six will be able to describe the probabilities of chance experiments using both small and large numbers.  They will benefit form opportunity to use appropriate digital technologies (ACARA, 2015, ACMSP144 & ACMSP145)

 

Another concept in probability that is fundamental to understand is the sample space.  The sample space is the number of all possible outcomes.  In the tree diagram of the coin toss challenge linked (https://www.youtube.com/edit?o=U&feature=vm&video_id=QiCIPiTh4lo) there was a total of 8 combinations of heads and tails in specific orders, and or four combinations (3xH; 3xT; 2XH1XT; 2xT1xH) if it does not matter what order the coin lands. 

 

To determine the probability of an event occurring, the following formula can be used

 

P (event) =   The number of outcomes in which event can occur

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                             The total number of possible outcomes

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The probability of an event occurring and the probability of its compliment (event not occurring) must equal 1.  The more likely an event to occur, the closer the probability is to 1.  Probability can also be expressed as a percentage.  For example, 100% means it is certain to happen, 0% is when the event is impossible.   The above essentially gives a percentage of how likely it is to occur.  If there are multiple events occurring, to discover the possibility of them both occurring at same time is the probability of one event multiplied by the probability of the other event. 

 

Tree diagram looks like branches of a tree and is used to illustrate the possibility of a particular outcome.  An example of this diagram can be seen in my coin toss video (https://www.youtube.com/watch?v=QiCIPiTh4lo.  This diagram gets its name as it resembles the branches off a tree. Students could then use this to determine the probability out of 8 each chance has of occurring (3 heads would be 1/8 and 1 head and 2 tails would be 3/8).  Students will use fractions, decimals and percentages from year 6 to solve probability investigations).  This can be seen in content descriptor ACMSP144 (ACARA, 2015).