Bookies wail after Dettori's super seven

Occasionally unusual sporting outcomes provide an opportunity to discuss some mathematics in an applied setting. Such is the case with the horse racing feat accomplished by Frankie Dettori. Depending on their out-of-school experiences, some students will easily understand the odds of 25,095 to 1 and the payout to the punter. Others will need some assistance.

Unfortunately there is not enough information provided to work out the multiplicative effect of the seven races in determining the final odds. Senior students who have considered the independence of events might like to consider whether they believe that the seven races constituted independent events. From the comment made by Dettori about the odds on his horse in the seventh race changing from 12 to 1 to 2 to 1, it would seem that the punters and bookmakers did not consider the races independent events.

The formal relationship between odds and probability can be noted here. With odds of 25,095 - 1, what is the expected probability that Dettori's horses will win all seven races? (1/25096)

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