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Binomial or Not?

Age 16 to 18 Challenge Level:

Why do this problem?


Beyond learning to apply the binomial distribution formula, it is important for students to recognise when the binomial distribution is an appropriate model and when it is not.  The twelve situations offered cover a variety of misconceptions and misunderstandings with regards to the binomial distribution, as well as having some "real life" situations which could be reasonably modelled using the binomial distribution, even if it is not exact.  This aims to help students delineate the boundaries between examples and non-examples of binomial distribution situations, and thereby to improve their mental map of this topic.  It also forms a nice complement to Binomial Conditions, which asks why each of the conditions needed for a situation to be described by a binomial distribution are necessary: suitable examples for that problem can be found among these twelve situations.

Possible approach


This printable worksheet may be useful, and it could be cut up to make a card sort: Binomial or not.pdf

This could be run as a whole-class activity.  Show the situations one at a time to the students, and ask them to consider whether it is or is not described by the binomial distribution.  They could then vote on their ideas, and one person from each side could then justify the reasoning for their choice.  The activity has some prompting questions at the start of the problem page, and these could then be used to probe further.

An alternative approach is to cut out the sheets and to use this as a sorting activity.  This has the advantage that a few of the situations are fairly similar, but the small differences are very significant.  This could help students improve their ability to discriminate between binomial and non-binomial situations.  After they have sorted the cards into binomial and non-binomial groups, they could then be asked the prompting questions from the problem page. Students could also be invited to create their own similar situations and challenge each other to sort them in the same way.

Key questions
 

In what situations is the binomial distribution a suitable model?
What can cause the binomial distribution to fail to be a suitable model?

Possible extension


In what situations is the binomial distribution a good approximation?
Once students are confident at deciding when a situation can be modelled with a binomial distribution, they could work on Binomial Conditions.

Possible support


Write down the conditions for the binomial distribution.  Can you match the conditions up to the situation?  If so, it's binomial, if not, it almost certainly isn't.  Which condition fails?