Consider a person wanting to play a game of dice. Whenever he wins a game he gets 1 dollar from his opponent. If he looses he gives his opponent a dollar.
He starts by rolling the dice 4 times hoping to get at least one 6. After a number of tries he thinks that his chances would be better if he rolls two dice 24 times hoping to get at least two 6.
The question is: from where could he have gotten the idea of changing the number rolls (and dice) so as to improve his chances of winning some money?
I have calculated both probabilities using the binomial-method. The opposite of at least one six (in 4 rolls) is no six at all and the opposite of at least two six (in 24 rolls) is no two six at all. I have calculated the probabilities. But how does a satisfacotry answer come from that?
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