Pick from the Pot


The pot contains 10 counters which are being randomly removed and replaced. How many of each colour do you think are in the pot?

A Mathematics Lesson Starter Of The Day

Topics: Starter | Data Handling | Probability

  • Dylan H, Charnwood Primary Year 6
  • It was a good task and very challenging at the same time.
  • Mr Lunnon, Bluecoat Academy
  • Can you remove/give the option to remove the comment "the pot contains 10 counters....." please. I like to use this for a wide range of activities and have to tell pupils to ignore that statement! Thanks.

    [Transum: A button has been added above Mr Lunnon.]
  • Phill O'Donnell, Chesterfield, Derbyshire
  • Hi, great starter and opener. It would be really useful to have a pause button!

    [Transum: A pause button has been added above. Please note that you can also vary the total number of counters in the pot and the speed of the picking using the controls at the bottom of this page.]
  • Alison Tanner, Darrick Wood Juniors
  • Love this starter, but for those children who find it harder to grasp a concept I'd love the abiity to see inside the pot!

    [Transum: Good idea Alison. That will be built into the next update of this page.]
  • M. Smith, Seaford
  • Can you please provide a solution to this starter? We have had a variety of answers and lots of discussion.

    [Transum: Glad to hear that there has been lots of discussion. Answers are only available to teachers when they are signed in and will appear lower down this page.]
  • Mr. L.J.Jackson, Saint Bede's Redhill
  • Could you build in a table of results? With the idea that the more results you collect the more reliable your relative frequency will be?
  • The Math Book,
  • In his book 'Ars Conjectandi', Bernoulli estimates the proportion of white balls in an urn filled with an unknown number of black and white balls. By drawing balls from the urn and 'randomly' replacing a ball after each draw, he estimates the proportion of white balls by the proportion of balls drawn that are white. By doing this enough times, he obtains any desired accuracy for the estimate.

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
Click here to enter your comments.

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[Notes for Teacher: The film will go on for ever! It shows a red, green or blue counter being taken from the pot by random selection but in proportion to the number of red, green and blue counters in the pot. Students might make a tally chart to see the relative numbers of counters being pulled out of the pot then divide 10 in the same ratio.]

Online Maths Shop

Laptops In Lessons

Teacher, do your students have access to computers such as tablets, iPads or Laptops?  This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments:


However it would be better to assign one of the student interactive activities below.

Laptops In Lessons

Here is the URL which will take them to a student probability activity.


Student Activity



Change the number of counters in the pot:

You can vary the speed of the animation by sliding the handle below to the left or to the right.




Bertrand’s Paradox

We ask for the probability that a number, integer or fractional, commensurable or incommensurable, randomly chosen between 0 and 100, is greater than 50. The answer seems evident: the number of favourable cases is half the number of possible cases. The probability is 1/2.

Instead of the number, however, we can choose its square. If the number is between 50 and 100, its square will be between 2,500 and 10,000.

The probability that a randomly chosen number between 0 and 10,000 is greater than 2,500 seems evident: the number of favourable cases is three quarters of the number of possible cases. The probability is 3/4.

The two problems are identical. Why are the two answers different?

Joseph Bertrand, Calcul des probabilités, 1889 (translation by Sorin Bangu) presented by Futility Closet.



Curriculum Reference

See the National Curriculum page for links to related online activities and resources.


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