# classical probability question

At the race course, Adam meets his friend Bruce. Bruce offers to receive bets from Adam for a race involved two horses named Gold and Diamond. Bruce suggests even odds for betting on both horses.

However, a bookmaker also offers odds for the same race. The bookmaker gives odds of 3 to 1 for Gold and 0.5 to 1 for Diamond.

Not to disappoint Bruce, Adam has decided to place bets with the bookmaker, as well as with his friend Bruce.

Adam has \$10 in his pocket and is considering the following strategies: (I) Bet \$4 for Gold with the bookmaker and \$6 for Diamond with Bruce. (II) Bet \$5 for Gold with Bruce and \$5 for Diamond with the bookmaker. (III) Bet \$6 for Gold with Bruce and \$4 for Diamond with the bookmaker. (IV) Bet \$7 for Gold with the bookmaker and \\$3 for Diamond with Bruce.

Which strategy is preferable if Adam’s foremost goal is to minimize the possibility of any loss?

A. (I) B. (II) C. (III) D. (IV)

E. It does not matter. Adam should just randomly choose a strategy

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Are these British odds or mathematical odds? In other words, do the bookmaker's odds suggest Diamond or Gold is the odds-on favorite? –  Henry Sep 14 '12 at 14:29