Answer to Question #351049 in Statistics and Probability for Bob

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

a) Assume that the sample space consists of a win for each of the 16 different horses

$$1(0.3)+2(0.2)+1(0)+(16-4)(0.05)=1.3>1$$

The probabilities must sum to $1.0.$

b) Even Desert Pansy must have a non-negative probability of winning.

So Joe is incoherent, albeit profitable!