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For younger learners

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Sample

Age 14 to 16
ShortChallenge Level Yellow starYellow star
Secondary curriculum
  • Problem
  • Solutions

Here are three populations:

      


An opportunity sample, a systematic sample and a random sample was taken from each.
Can you match the samples to the populations?


Opportunity samples (a convenient block of 9 squares was chosen):

      


Systematic samples (every 11th square was chosen to give a sample size of 9):

      


Random samples (9 squares were chosen at random):

      



You can find more short problems, arranged by curriculum topic, in our short problems collection.

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Coin Tossing Games

You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by a head (you win). What is the probability that you win?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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