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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Two's Company

### Why do this problem?

### Possible approach

### Key questions

### Possible support

### Possible extension

## You may also like

### Master Minding

### Flippin' Discs

### Cosy Corner

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

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Age 11 to 14

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

This problem offers an opportunity to explore and discuss two types of probability: experimental and theoretical. The simulation generates lots of experimental data quickly, freeing time to focus on predictions, analysis and justifications.

Demonstrate the interactivity by running it a few times, explaining that to win, the two blue balls need to touch.

Invite students to estimate the probability of winning. Allow students some thinking and discussion time in pairs before bringing them together to state their initial conjectures.

Students may find these Recording Sheets useful for exploring different possible outcomes.

Record their conjectures on the board and then run the interactivity a few hundred times.

Then revisit students' conjectures and discuss which ones matched the experimental data, before rounding the activity off by discussing which methods for recording the different combinations were both successful and efficient.

Are there efficient systems for recording the different possible combinations?

What counts as a different outcome?

If the yellow and red marbles are in the same position but the blue marbles swap places, does that count as a different outcome?

This problem could be tackled as a follow-up to Cosy Corner

Teachers may want to use this recording tool to gather the results of other similar experiments that their students are carrying out:

A follow-up problem could be The Better Choice

Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?

Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?