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Master Minding

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?

Flippin' Discs

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

Cosy Corner

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

Two's Company

Age 11 to 14 Challenge Level:


Why do this problem?

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.

Possible approach

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.

Key questions

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?

Possible support

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:

Possible extension

A follow-up problem could be The Better Bet