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.

Click here for Notes for Teachers.

Click here to download the Twos Company poster.

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.

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