How many times must a die be thrown to get four consecutive sixes? More generally, and more precisely,Ql. What is the expected number of times we must throw a die to get n consecutive sixes?The answer, rather suggestively for the numerologically inclined, turns out to beAl. The expected number of throws is 6 + 6~2 + 6~3...+6~n.In some well-known dice games players throw several dice at the same time: in craps a pair (brace) of dice is thrown, while in yahtzee, yam and balut, up to five dice are thrown at a time. However, Q1 is not the same as Q2. What is the expected number of times we must throw a set of n dice until in one throw all n turn up six? Here the number of possible outcomes for one throw is 6" (think of n dice all of different colours), and all outcomes are equally likely, so the answer is simply A2. The expected number of throws of a set of n dice is 6~n.
展开▼
