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Fixing the Odds

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

You have two bags, four red balls and four white balls. You must put all the balls in the bags although you are allowed to have one bag empty. Your friend chooses a bag at random and then chooses a ball at random from that bag. How should you distribute the balls between the two bags so as to make the probability that your friend will choose a red ball as small as possible and what will the probability be in that case?

How should you distribute the balls so as to make the probability of choosing a red ball as large as possible and what will the probability be in that case?

What happens if you have two bags, a hundred red balls and a hundred white balls?

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Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags. The marble is blue. What is the probability that it was removed from bag A?

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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