The mathematical genii apply their Statistical Wizardry to Basketball

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Situation

The manager of a professional basketball team is having a tough decision in choosing which of his two top scorers this season are better at free-throw shots. The final decision will go towards picking the team for Saturday's Cup Final match.

On a training session one week before the match the coach decides to "go all out" and bring some mathematical genii in to model a situation where Lee Grimes and Dominic Aspbury, the goalscorers, will shoot at the basketball net.

The mathematical genii are students from Cambridge and are benefiting from this opportunity in that they will be able to show evidence of coursework for their final exam. Their coursework will be using their abilities to collect data and "test the appropriateness of a probability model" on a real situation whilst the coach's aim will be to pick the better of the two players for the "big game."

If the random variables X and Y count the number of independent trials before the event, having a probability p, occurs then X and Y have geometric distributions:

P ( X = r ) = q r - 1 p where r