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The Better Choice

Age 14 to 16
Challenge Level Yellow star
Secondary curriculum
  • Problem
  • Getting Started
  • Student Solutions
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The Better Choice printable sheet
 

Here are two games you can play. If you played both games the same number of times, in which game would you expect to win more points?

Game 1:

In every round you flip four coins and win 3 points if you get two heads and two tails 

or

Game 2:

In every round you spin three 1 - 6 spinners and win 2 points for every six that appears

The interactivity below allows you to simulate both games (including versions in which it 'costs' a point to play each round).

Can you explain the result of playing each game a large number of times?

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Marbles and Bags

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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