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#### Article Title

CALCULATING DEPENDENT PROBABILITIES

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#### Abstract

In the 2004 European soccer competition France were one of the favourites to win the World Cup and Thierry Henry, their star forward, was one of the favourites to be top goal scorer. Bookkeepers were offering odds of 4 :1 on France winning the competition and odds of 8: 1 on Thierry Henry being the top scorer. A large number of punters went into betting shops in the United Kingdom and made a single bet that France would win the competition and that Thierry Henry would be top scorer. The counter clerks in the betting shops accepted the bets and punters making the bets believed that a £1 stake would bring a return of £42. ( A £1 stake on France winning the competition at odds of 4 : 1 gives £5 (=£4 plus return of the £1 stake). The £5 then being bet on Thierry Henry being top scorer at odds of 8 :1 gives £45( = £40 plus £5.) In general if a bet is made on two outcomes and the odds of each outcome are m : 1 and n : 1 then the return on a £1 stake is £(m + 1)(n + 1)).

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