A container holds 4 yellow balls, 2 blue balls and a red ball. The balls are identical in all ways except colour. When you shake the container the balls settle into a hexagonal pattern as shown in the diagram.

You win if two blue balls touch.

How many different ways can the two blue balls fall?

How many outcomes result in a win?

What is the probability of winning?

You might find this sheet useful.

See the NRICH site for an interactive game to explore this problem.

### 3 Responses to Two’s Company

1. Mabhamba Mabhamba says:

My learners attempted it using probability rules. I tried it with Grade 10 learners. They took one learner and label him as blue and count how many times will another blue touch the stationery blue.
I enjoyed working with with my learners with this problem.

2. Esme Meyer says:

My learners are still very confused when it comes to probability. They only time they seem to grasp it, is when we do a practical activity. Perhaps we need to be given more exposure on how to better present lessons on probability.