Answer to Question #351006 in Statistics and Probability for EDD

Question

5. QUESTION:

You consult Joe the bookie as to the form in the 2.30 at Ayr. He tells you that, of 16 runners, the favourite has probability 0.3 of winning, two other horses each have probability 0.20 of winning, and the remainder each have probability 0.05 of winning, excepting Desert Pansy, which has a worse than no chance of winning. What do you think of Joe’s advice?

Answer 1

Assume that the sample space consists of a win for each of the $16$ different horses. Joe’s probabilities for these sum to $1.3$ (rather than unity), so Joe is incoherent, albeit profitable! Additionally, even “Dobbin” has a non-negative probability of winning.