Probability [ S3.1 Core Plenary] An old fairground game used to involve rolling a coin at random on a board with parallel lines on it. A prize was won if the coin did not land on a line. Amber finds an expression giving the probability of a coin diameter c cm not landing on one of the lines which are d cm apart. It is: . Amber wants to test it so she draws some parallel lines 4 cm apart and rolls a 1p coin, diameter 2 cm, on it. She records whether or not she wins. Here are her results. W represents win and L lose. Do these results fit the formula? Explain why.   Preamble A relatively simple activity involving comparing theoretical and experimental probabilities, together with some informal appreciation of the randomness of situations. As a possible extension, pupils could be shown how to derive the probability. A simple diagram (see below) shows this at an intuitive level. Checking the formula through practical investigation would make a worthwhile homework task and allow a wide range of line widths to be investigated. Possible content Using simple formulae, calculating experimental probabilities and comparing experimental and theoretical probabilities. Resources Depending on circumstances, pupils could experiment for themselves. Solution/Notes Theoretical probability = 0.5 and experimental probability = so the results broadly fit the formula. L W Original Material © Cambridge University Press 2010 Original Material © Cambridge University Press 2010