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Two ordinary dice are thrown repeatedly; the outcome of each throw is the sum of the two numbers. Joe Shark, who says that 6 and 8 are his lucky numbers, bets even money that a 6 will be thrown before the first 7 is thrown. If you were a gambler, would you take the bet? What is your probability of winning? Joe then bets even money that an 8 will be thrown before the first 7 is thrown. Would you take the bet?

Having gained your confidence, Joe suggests combining the two bets into a single bet: he bets a larger sum, still at even odds, that an 8 and a 6 will be thrown before two 7s have been thrown. Would you take the bet? What is your probability of winning?

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