Planning tool

Students:

• represent probability on a probability scale from zero to one
• use the terms impossible, unlikely, equal chance, likely and certain
• express probabilities using fractions, decimals and percentages
• describe whether the probability of an event is random and/or fair
• explain their reasoning when discussing chance activities
• use manipulatives to model their solution and thinking.

Some students may:

• have difficulty explaining why an event is random and what the likely outcomes may be. Check for student understanding by investigating a die roll where one person wins if the number is odd while the other wins if the roll is an even number. Change the parameters so that they then use two dice, and one wins if the dice total 8 or more, while the other wins if it is 7 or under. Listen to them argue mathematically as to whether the game is random, fair or unfair.
• be able to express the probability of an event occurring using the language of chance but be unable to assign a value as a fraction, decimal or percentage. Use a number line and discuss fractions, decimal or percentages, starting with 50% as an equal chance, 0% as no chance and 100% as a certainty. Use enabling prompts to scaffold the learning.

1. The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

• We are learning about chance.
• We are using probability in real-life contexts.

Why are we learning about this?

• Probability is the chance or the likelihood of something happening. Understanding probability is important as it occurs in many areas of work and our daily lives.

What to do

Work out these problems. Give reasons for your answers to explain how you worked it out.

1. If 30% of blood donors have ‘type A’ blood and you contact 100 people.
   
   1. What is the likelihood of finding a donor with ‘type A’ blood?
   2. Two How many people out of the 100 would you expect to have ‘type A’ blood?
   3. You need 150 donors with ‘type’ A blood. How many people would you expect to call to find 150 people with ‘type A’ blood?
2. A lake contains two types of fish: brown trout and rainbow trout. The fish in the lake are 60% brown trout and 40% rainbow trout. Anglers catch the fish and release them back into the lake.
   
   1. Which fish are you more likely to catch?
   2. If you catch 10 fish, how many of each type are you likely to have?
   3. An angler catches 9 rainbow trout and 1 brown trout. Is this what you would expect? Explain your answer.
3. A netballer has a great record of goal shooting. Nine times out of 10, the netballer scores a goal when they stand within 2 metres of the goals. Beyond 2 metres from the goal, they have an equal chance of missing or getting a goal.
   
   1. What is the likelihood they score a goal when standing 1 metre from the ring? Write this as a fraction, decimal and percentage.
   2. In a typical game, the netballer shoots at goal 50 times. How many goals would you expect to be scored if 30 of the shots are taken within 2 metres of the goal? Create a table or model to show your results.

Success criteria

I can:

• identify all possible outcomes of a chance experiment
• assign probabilities to a simple event.