M4.6.5 For the adult
Picking without putting back
A bag has 5 red and 3 blue counters. I take one, keep it, and take a second. What is the chance that both are red?
What this chapter teaches
When a counter is kept, the bag changes. The second pick is not independent of the first, so the branches of the second stage show a smaller bag. Multiply along a path, add the paths that make the event, and check that all the ends add to 1.
Three questions to ask
There is no one right wording. Listen for the idea.
- Why do the chances for the second pick change when the first counter is kept?
- How can you check that a tree for two picks has no slip in it?
- Would the chance of two reds be higher or lower if the counter were put back, and why?
After the chapter, the learner can
- Draw a tree diagram where the first pick changes the second
- Find the chance that two picks from a bag are both red
What they copy into their notebook
Without putting back, the bag shrinks. Second pick: one fewer counter in all, and one fewer of the colour taken. Multiply along paths. All ends add to 1.