In this activity your students will make some predictions about chance events. They will make some assumptions and then use reasoning to work out how likely it is that different colored balls would be pulled out from a bag.
For this activity you will need pictures of bags containing different colored balls and in different proportions. For example:
- Three red and seven blue;
- Five red and five blue;
- Six red and four blue;
- Six red and six blue; and
- Six red and fourteen blue.
I have made up some of these pictures for you, just click on the picture below to download your copy.
Ask your students to choose a bag from which they are equally likely to select a red or a blue ball. Ask them:
- What is the chance of getting a red from that bag?
- What is the chance of getting a blue from that bag?
- Are there any other bags where there is an equal chance of getting a red or a blue ball?
- What is the chance of getting a red from that bag?…or blue?
- Is it the same chance as for the other bag?
Highlight that 5 chances in 10 and 6 chances in 12 are both one half. Red and blue are equally likely, so each has half a chance of being selected.
More and less likely
Ask your students if they are more likely to get red or blue from the first bag (three red and seven blue). Repeat for the other bags. Get your students to sort the bags where red is equally likely as blue, those where red is less likely than blue and those where red is more likely than blue. Explain that when red is less likely than blue then we would expect the chance to be less than half, and when red is more likely than blue then we would expect the chance to be more than half.
Ask students what chance is there of getting red from the first bag (3 chances in 10). Ask: is this less than half?